You usually apply yourself with the support of your PI.
As an undergraduate student, I participated in the same conference 3 different years, but I can only speak for this one conference.
The Society for Neuroscience has a yearly giant (33k people) convention and each year they have a symposium called FUN (Faculty for Undergraduate Neuroscience) that you can present at as a student. Basically everyone gets in as long as you submit an abstract by October, or whatever the deadline is. At my school, students who were presenting at a conference were eligible to apply for travel grants to cover expenses and the conference offers undergraduate travel grants as well. The real-deal is the main conference, which is a lot more difficult to get into and requires a serious submission in May, but you take what you can get and the undergraduate symposium is awesome practice for the real thing 🙂
Edit: Also, a lot of summer programs have a poster presentation at the end of the summer. These are not as fun to go to as the conferences (for one thing, you don't get free swag 😉) or as impressive on your resume, but it's still a poster presentation.