How do you request a friend

Depends
If they're not currently using MFP
community > invite friends
enter their email to send them an invite to join

If they ARE a member of MFP and you know their username
www.myfitnesspal.com/their_username
when you are viewing their profile you'll see a green "add friend" along with "send message" and perhaps "view diary" depending on their settings (if diary is public then you'll see view diary even if not friends, if it's shared with friends only you won't see it until you are actually friends within MFP)

if you see someone you might want to friend click to view the profile, it will be a blue button, middle of the page next to the pic.

Thank you