The big thing with pushing is, as dwtim noted, it does tend to help you relax the anus. You don't have to push, but don't go the other way and think that pushing is connected with inexperience. I sometimes push and sometimes don't, depending on the situation.
Once the toy/penis/other body part is inserted take some time to let things rearrange and relax. Once that's done you shouldn't need to continue to push out, but if you're having problems with the toy "hanging up" on something inside pushing for a while can help to move things around. The big thing is to not tense up the anus unless you're more experienced and are doing it intentionally (and can relax it just as easily).
If you're doing penile-anal sex pushing out from time to time can toss things up a bit, as can occasional clenching of the anus, but with a dildo or finger your partner doesn't really notice.