When you first begin working, most bigger firms will have the Lexis/Westlaw reps come in and do a training. The reps give you a 1 week free trial for Westlaw/Lexis respectively. Once that runs out, then you begin using the pay account the firm /reps assign you.
Also, once a week the Westlaw rep comes and during that time span anyone can do research on Westlaw for free in the firm library or training room or whatever. This is the same for Lexis. This is the best time to get your research done.
Another little tidbit, when you first begin working, don't use a lot of Lexis/Westlaw after your week expires. Even during your free week, use it to double check your library research. You can find basically everything you need in the library.
Small story: last summer, my post 1L summer, one of the 2Ls clerking there was using the pay Westlaw account before our training. He didn't know that he had chosen the pay-per-minute option and racked up a $1400 research fee for the client. Long story short, the firm worked it out with him and the Westlaw, he got an offer, everything's dandy. Honest mistakes are ok!