You can access the voting page from either 'My Challenges' or the top of the Challenge page:
My Challenges:
1) Find the challenge you want to vote in and tap the "Vote" button.
2) Tap on a photo to add it to your picks.
3) Scroll down to load photos to vote on.
4) Once you're done selecting press the 'Submit' button.
Open Challenges (challenges you didn't join):
1) Find the challenge you want to vote for.
2) Tap the "Vote" button (the icon with the "check-mark").
3) Tap on a photo to add it to your picks.
4) Scroll down to load photos to vote on.
5) Once you're done selecting press the 'Submit' button.