@earthling's accepted answer -- to use the passive voice -- is perhaps the convention in certain disciplines, but it is crucial to note that the active voice is the convention in others. Using the passive voice will make a paper sound daft and amateurishly pompous in certain communities.
My preference is very much for the active voice, first person (plural in almost all cases). This is also the most prevalent convention in my community (applied CS).
The strongest argument (and it is a very strong one!) against passive voice is that it removes all responsibility from the doer: it leaves ambiguity as to who did what, which is crucial for proper attribution in scientific writing.
The methods of Franklin et. al. were taken. The software was implemented in Java.
Who implemented the methods? The authors of the current paper or Franklin and his pals? Who should be contacted if there's errors in the software? Who's to credit and who's to blame?
Even aside from ambiguity, in the hands of a deceptive author, the passive voice could be used to subtly claim credit for others' work.
The methods of Franklin et. al. were taken. These methods were extended to incorporate the inputs previously described.
... the authors make it sound a bit like they did the extending, but maybe they didn't?
The second argument against the omnipresent passive voice is more subjective: that for many people (including me), it sucks to read, it sucks all humanity from the writing, any modesty it provides is entirely false, and it just generally sounds pompous.
So if using the active voice, which person to use? Again this is convention, but talking about yourself in the third person is again considered silly in many communities (although mandatory in some journals!). Also using the third-person can introduce the same ambiguities regarding what was your work and what was the work of others:
The methods of Franklin et. al. were taken. The authors extended these methods to incorporate the inputs previously described.
Leaving convention aside, first person is the only voice with a clear objective argument in favour of it: it avoids ambiguity as to who did what!
All arguments for passive voice refer to subjective matters of style or (false) modesty. (Aside from which, I feel that first person active voice is a more natural style!)
However, you should follow the convention of the venue you are submitting the paper to!
See these letters to Nature, for more on the debate.
(The second author sounds ridiculously pompous to me.)