You can Enter any contest in the appropriate thread. We are currently between Contest, and as such there are none running right now, but check back in about two weeks time, a new prose and poetry contest should start then.
As for Members’ Choice, this is not a contest, but rather a place where members can nominate work from other members that they liked, and then every three months they can vote for their favourites from the nominated work.
Further information can be found in the FAQ, and if that does not help do ask.
Quis custodiet ipsos custodes?