Load the package footmisc (as suggested by jon) with the option norule to suppress the rule and hang to have the indentation on every line.
Then adjust the values of the lengths \footnotemargin (for the indentation) and \skip\footins (for the spacing between footnotes and text).
\documentclass{article}
\usepackage{lipsum} % just for the example
\usepackage[norule,hang]{footmisc}
\setlength{\footnotemargin}{1em}
\setlength{\skip\footins}{3em}
\begin{document}
\lipsum[1-3]\footnote{\lipsum[1]}
\lipsum[1-5]
\end{document}

If you also want your footnotes to be bottom-aligned with the page, add the option bottom when loading footmisc:
\usepackage[bottom,norule,hang]{footmisc}
\usepackage[hang]{footmisc}. (But it is always better to provide a MWE: it helps you get the help you want/need more quickly becuase it helps people who want to help you see where the roots of the problem lie.) – jon Dec 14 '14 at 05:14http://tex.stackexchange.com/questions/126877/how-can-i-align-a-multiple-line-footnote-text-right-to-the-footnote-mark?rq=1
– user68964 Dec 14 '14 at 05:25