To submit a poem to a contest, first find one that is of interest to you. Once you have found a contest, submit a poem and, before hitting "save", select the relevant contest in the dropdown menu labeled "contest" (contests that are open will start with "Open to new participants" and will be on the top of the list). There's never a cost to enter. There's often a prize, and if you win, you'll be listed as the contest winner forever, and fellow poets will see, in your profile page, what contests you have won.