The answer is now updated for the date handling in newer biblatex versions >= 3.6, lots of what had to be done manually before will now be done automatically. Check the edit history for earlier versions.
This is quite a full-on question, but I will try to answer it anyway. This answer mainly deals with the bibliography output. For citations additional modifications and configurations might be necessary, but what needs to be done strongly depends on the used style, there is no universal answer. For numeric citation styles the example below will of course work without further modification.
Declare new fields, and the new entry types and their fields
First, when declaring the data model, we need to make sure biblatex actually knows the type of the fields/lists we declare (this is done via the optional argument to \DeclareDatamodelFields). You can read much more about this in §4.5.4 Data Model Specification, p. 212 of the biblatex documentation.
There are two main types for entry field: field and list. fields usually hold one value, while lists can hold more items separated by an and in the .bib file (see also §2.2.1 Data Types, p. 15).
I declared the sitekey and sitetopic to be literal fields (such as the title field).
askp and ansp are clearly name lists (even though in this context the list will probably only ever hold one item).
A lot of the fields you are asking for seem to revolve about dates, so there are askdate, ansdate, askeditdate, anseditdate and their dateparts (which will be created automatically, but they still need to be added to \DeclareDatamodelEntryfields manually).
Finally, I decided the ids should be verbatim fields.
\begin{filecontents}{stackexchange.dbx}
\DeclareDatamodelEntrytypes{stackexchange}
\DeclareDatamodelFields[type=field,datatype=literal]{
sitekey,
sitetopic,
}
\DeclareDatamodelFields[type=list,datatype=name]{
askp,
ansp,
}
\DeclareDatamodelFields[type=field, datatype=date, skipout]{
askdate,
ansdate,
askeditdate,
anseditdate}
\DeclareDatamodelFields[type=field, datatype=verbatim]{
askid,
askpid,
anspid,
ansid,
}
\DeclareDatamodelEntryfields[stackexchange]{
sitekey,
sitetopic,
askid,
askp,
askpid,
ansp,
anspid,
ansid,
askyear,
askmonth,
askday,
ansyear,
ansmonth,
ansday,
askedityear,
askeditmonth,
askeditday,
ansedityear,
anseditmonth,
anseditday,
title}
\end{filecontents}
The \DeclareDatamodelEntryfields just makes those fields relevant to @stackexchange known to that entry type.
Declare new bibliography strings (if necessary)
We also want to display words like 'asked' and 'answered', instead of hard-coding them, localisation with .lbx files is the way to go. This is only necessary if you wish to include strings in the output. It is not necessary to include a string for each field you define. The fact that the name of some bibstrings coincides with the name of some fields is purely accidental. There is no requirement to define bibstrings for certain field types.
The most complete way to define new strings is by means of an .lbx file, because that method allows you to define long and short forms of the strings. You can also define new strings directly in the preamble, but then you can only give one form that is used as short and long version.
Our new localisation file english-stack.lbx inherits everything from english.lbx but adds asked, answered and edited as bibstrings.
\begin{filecontents*}{english-stack.lbx}
\ProvidesFile{english-stack.lbx}[2014/05/07 english with additions for stackexchange]
\InheritBibliographyExtras{english}
\NewBibliographyString{asked,answered,edited}
\DeclareBibliographyStrings{%
inherit = {english},
asked = {{asked}{asked}},
answered = {{answered}{answered}},
edited = {{edited}{edited}},
}
\end{filecontents*}
We have to tell biblatex to use that language definition
\DeclareLanguageMapping{english}{english-stack}
Defining the bibliography output
Then finally, we can go on to define the bibliography driver. The bibliography driver is the main definition that decides how the entry is printed in the bibliography. A bibliography driver typically consists of calls to several bibliography macros as well as calls to punctuation and printing commands.
Field formats
Field formats define the formatting of each printed field. We avoid hard-coding anything and use the macros provided by biblatex.
So instead of wrapping \printfield{title} in \mkbibquote, we define the field format to do so.
We use \setunit for punctuation and \bibstrings in lieu of hard-coded words.
\DeclareFieldFormat[stackexchange]{title}{\mkbibquote{#1\isdot}}
\DeclareFieldFormat{askpid}{%
\mkbibparens{\ifhyperref
{\href{http://tex.stackexchange.com/users/#1}{\nolinkurl{#1}}}
{\nolinkurl{#1}}}}
\DeclareFieldFormat{anspid}{%
\mkbibparens{\ifhyperref
{\href{http://tex.stackexchange.com/users/#1}{\nolinkurl{#1}}}
{\nolinkurl{#1}}}}
\DeclareFieldFormat{askid}{%
\mkbibparens{\ifhyperref
{\href{http://tex.stackexchange.com/q/#1}{\nolinkurl{#1}}}
{\nolinkurl{#1}}}}
\DeclareFieldFormat{ansid}{%
\mkbibparens{\ifhyperref
{\href{http://tex.stackexchange.com/a/#1}{\nolinkurl{#1}}}
{\nolinkurl{#1}}}}
As an added bonus, the id fields now link to the proper stackexchange site.
\newbibmacro*{stackexchangequestion}{%
\printfield{title}%
\setunit{\addspace}%
\printfield{askid}%
}
Bibliography macros
Bibliography macros can be used to compartmentalise the output definitions.
No formatting should be applied to the \printfield commands, formatting is dealt with by \DeclareFieldFormat.
\newbibmacro*{stackexchangeask}{%
\bibstring{asked}%
\setunit{\addspace}%
\printaskdate%
\iffieldundef{askedityear}%
{}
{\printtext[parens]{%
\bibstring{edited}%
\setunit{\addspace}%
\printaskeditdate}}%
\setunit{\addspace}%
\bibstring{byauthor}%
\setunit{\addspace}%
\printnames{askp}%
\setunit{\addspace}%
\printfield{askpid}%
}
\newbibmacro*{stackexchangeans}{%
\bibstring{answered}%
\setunit{\addspace}%
\printansdate%
\iffieldundef{ansedityear}
{}
{\printtext[parens]{%
\bibstring{edited}%
\setunit{\addspace}%
\printanseditdate}}%
\setunit{\addspace}%
\bibstring{byauthor}%
\setunit{\addspace}%
\printnames{ansp}%
\setunit{\addspace}%
\printfield{anspid}%
}
\newbibmacro*{stackexchangesite}{%
\printfield{sitetopic}}
Bibliography driver
The driver defines the final output structure. Usually a driver makes heavy use of bibmacros, but it need not do that.
\DeclareBibliographyDriver{stackexchange}{%
\usebibmacro{bibindex}%
\usebibmacro{begentry}%
\usebibmacro{stackexchangequestion}%
\newunit\newblock
\usebibmacro{stackexchangeask}%
\newunit\newblock
\usebibmacro{stackexchangeans}%
\newunit\newblock
\usebibmacro{stackexchangesite}%
\newunit\newblock
\usebibmacro{finentry}}
MWE
\RequirePackage{filecontents}
\begin{filecontents*}{\jobname.bib}
@stackexchange{se:l3help,
sitetopic = {tex},
title = {What can \textit{I} do to help the \LaTeX3 Project},
askdate = {2012-02-26},
askid = {45838},
askp = {Brent Longorough},
askpid = {344},
ansp = {Frank Mittelbach},
anspid = {10109},
ansdate = {2012-03-01},
ansid = {46427},
}
\end{filecontents*}
\begin{filecontents}{stackexchange.dbx}
\DeclareDatamodelEntrytypes{stackexchange}
\DeclareDatamodelFields[type=field,datatype=literal]{
sitekey,
sitetopic,
}
\DeclareDatamodelFields[type=list,datatype=name]{
askp,
ansp,
}
\DeclareDatamodelFields[type=field, datatype=date, skipout]{
askdate,
ansdate,
askeditdate,
anseditdate}
\DeclareDatamodelFields[type=field, datatype=verbatim]{
askid,
askpid,
anspid,
ansid,
}
\DeclareDatamodelEntryfields[stackexchange]{
sitekey,
sitetopic,
askid,
askp,
askpid,
ansp,
anspid,
ansid,
askyear,
askmonth,
askday,
ansyear,
ansmonth,
ansday,
askedityear,
askeditmonth,
askeditday,
ansedityear,
anseditmonth,
anseditday,
title}
\end{filecontents}
\documentclass[english]{article}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[datamodel=stackexchange,backend=biber]{biblatex}
\usepackage{hyperref}
\addbibresource{\jobname.bib}
\begin{filecontents}{english-stack.lbx}
\ProvidesFile{english-stack.lbx}[2014/05/07 english with additions for stackexchange]
\InheritBibliographyExtras{english}
\NewBibliographyString{asked,answered,edited}
\DeclareBibliographyStrings{%
inherit = {english},
asked = {{asked}{asked}},
answered = {{answered}{answered}},
edited = {{edited}{edited}},
}
\end{filecontents}
\DeclareLanguageMapping{english}{english-stack}
\DeclareFieldFormat[stackexchange]{title}{\mkbibquote{#1\isdot}}
\DeclareFieldFormat{askpid}{%
\mkbibparens{\ifhyperref
{\href{http://tex.stackexchange.com/users/#1}{\nolinkurl{#1}}}
{\nolinkurl{#1}}}}
\DeclareFieldFormat{anspid}{%
\mkbibparens{\ifhyperref
{\href{http://tex.stackexchange.com/users/#1}{\nolinkurl{#1}}}
{\nolinkurl{#1}}}}
\DeclareFieldFormat{askid}{%
\mkbibparens{\ifhyperref
{\href{http://tex.stackexchange.com/q/#1}{\nolinkurl{#1}}}
{\nolinkurl{#1}}}}
\DeclareFieldFormat{ansid}{%
\mkbibparens{\ifhyperref
{\href{http://tex.stackexchange.com/a/#1}{\nolinkurl{#1}}}
{\nolinkurl{#1}}}}
\newbibmacro*{stackexchangequestion}{%
\printfield{title}%
\setunit{\addspace}%
\printfield{askid}%
}
\newbibmacro*{stackexchangeask}{%
\bibstring{asked}%
\setunit{\addspace}%
\printaskdate%
\iffieldundef{askedityear}%
{}
{\printtext[parens]{%
\bibstring{edited}%
\setunit{\addspace}%
\printaskeditdate}}%
\setunit{\addspace}%
\bibstring{byauthor}%
\setunit{\addspace}%
\printnames{askp}%
\setunit{\addspace}%
\printfield{askpid}%
}
\newbibmacro*{stackexchangeans}{%
\bibstring{answered}%
\setunit{\addspace}%
\printansdate%
\iffieldundef{ansedityear}
{}
{\printtext[parens]{%
\bibstring{edited}%
\setunit{\addspace}%
\printanseditdate}}%
\setunit{\addspace}%
\bibstring{byauthor}%
\setunit{\addspace}%
\printnames{ansp}%
\setunit{\addspace}%
\printfield{anspid}%
}
\newbibmacro*{stackexchangesite}{%
\printfield{sitetopic}}
\DeclareBibliographyDriver{stackexchange}{%
\usebibmacro{bibindex}%
\usebibmacro{begentry}%
\usebibmacro{stackexchangequestion}%
\newunit\newblock
\usebibmacro{stackexchangeask}%
\newunit\newblock
\usebibmacro{stackexchangeans}%
\newunit\newblock
\usebibmacro{stackexchangesite}%
\newunit\newblock
\usebibmacro{finentry}}
\begin{document}
\nocite{*}
\cite{se:l3help}
\printbibliography
\end{document}

To allow the use of askdate as labeldate, so the authoryear style (and other similar ones) does not print 'n.d.', we can use \DeclareLabeldate (§4.5.11 Special Fields, p. 238) as follows
\DeclareLabeldate{%
\field{date}
\field{eventdate}
\field{origdate}
\field{askdate}
\field{urldate}
\literal{nodate}
}
There also is \DeclareLabelname (p. 238) with a similar syntax, if you want to see either askp or ansp as the author in authoryear/authortitle styles.
\DeclareDatamodel*commands, which you would then pair with\newbibmacros and so forth. – jon May 07 '14 at 05:13:)– Sean Allred May 07 '14 at 14:51