Daily challenges refresh at 7PM PST, 10PM EST, or 6AM GMT.
They are readily accessible from the Main Menu, at the bottom of the screen under "Challenges".
The challenges I've had so far are fairly easy, with a few slightly more difficult ones.
Examples might be:
"Win one match-made game"
"Finish two match-made games as Isabel"
"Finish two match-made games as Cutter"
Once you complete a daily challenge, it will show you the countdown until they are next available.
There is a potential good glitch with this--you might get the achievement when you've only completed 1-2 of the challenges!
If you're having trouble with the win challenges, then Strongholds could be a good choice(found under multiplayer, "Rumble"), as you'll have a couple teammates who if they're good can make up for weak playing.
You can also boost this with a friend if necessary by simply searching at the same time as them--I was able to find my friends almost first try most of the time doing that.