The German LaTeX Wikibook contains a chapter about hyphenation -- here's the link.
babel Package
First of all make sure that you use the babel package. It loads hyphenation rules for the language you use.
hyphsubst Package
If you write in German maybe the hyphsubst package is a good option.
Manually Help LaTeX with the Hyphenation (Globally)
As stated here or here or here for example you can add specific hyphenation rules in the preamble of your document:
% needs babel package
\hyphenation{cryp-to-graphy lalala-la lolo-lolo-lulu}
Manually Help LaTeX with the Hyphenation (Locally)
I would recommend this as the last step when you finished your document. Then you can manually help LaTeX.
The command \overfullrule=2pt in the preamble will show you where LaTeX has a problem with hyphenation:
\documentclass{article}
\usepackage[ngerman]{babel}
% showframe to show the layout frames... :)
\usepackage[textwidth=50mm,showframe]{geometry}
% Show overfull boxes and lines (TeX primitive)
\overfullrule=2pt
\begin{document}
Lalalalalalala lalalalala lalalalala lalalalala
\end{document}

Here's a list of manual options:
\- Hyphenation a word only here and nowhere else (all other hyphenation rules are not valid anymore).
"- Hyphenation a word also here (the other hyphenation rules are still valid).
"= This produces a dash. Hyphenation is allowed here and the other hyphenation rules are still valid. Normally if a word contains a dash the dash is the only place where a hyphenation can occur.
"~ This produces a dash where no hyphenation is allowed.
"" Here a hyphenation can occur but no automatic hyphenation dash will be produced by LaTeX.
These commands work if you use ngerman option for babel. I do not
know how to make them work if you use other languages. Can somebody help me on this?
\documentclass{article}
\usepackage[ngerman]{babel}
% showframe to show the layout frames... :)
\usepackage[textwidth=50mm,showframe]{geometry}
% Show overfull boxes and lines (TeX primitive)
\overfullrule=2pt
\begin{document}
Lalalalalalala lalalalala lal"-lalala lalalalala
\end{document}

microtype Package
Stolen from the comments (@Henri Menke)!
The microtype package also improves hyphenation. The following cite is taken from the package manual:
Micro-typography is the art of enhancing the appearance and
readability of a document while exhibiting a minimum degree of visual
obtrusion. It is concerned with what happens between or at the margins
of characters, words or lines. Whereas the macro-typographical aspects
of a document (i.e., its layout) are clearly visible even to the
untrained eye, micro-typographical refinements should ideally not even
be recognisable. That is, you may think that a document looks
beautiful, but you might not be able to tell exactly why: good
micro-typographic practice tries to reduce all potential irritations
that might disturb a reader.
microtypepackage, which enables margin kerning and Hermann Zapf typography for enhanced line breaking. Using this package the right way considerably lowers the number of hyphenations. – Henri Menke Jan 30 '16 at 14:30\-you don't have to reword the paragraph or you can set \emergencystretch which does not change the spacing in good paragraphs or use microtype – David Carlisle Jan 30 '16 at 14:40babelwith the appropriate language option(s) to help LaTeX find additional permissible hyphenation points? Are the words that are running into the right-hand margin not very common and hence maybe not known to TeX's hyphenation algorithm? – Mico Jan 30 '16 at 14:41---) or the word attached to the em-dash (word---) is the thing that sticks out. – user12344567 Jan 30 '16 at 15:10microtypepackage did the trick. Thank you all for prompt responses. (I guess you can reproduce the comment in the form of an answer so I can accept it and so others can spot the solution immediately.) – user12344567 Jan 30 '16 at 15:16