Hey everyone first time poster and newbie DM, so me and 5 friends have recently picked up the 5E of D&D and we're loving it so far! My question is my players encountered an owlbear and they want to try and tame it for a mount, the monster manual says it's possible just not sure how to go about it? DC? What kind of checks? Ect. Any help would be awesome 
Just like everything else in D&D 5e, this depends on what approach your players take to accomplish that goal based on what complications you throw at them. When you are clear on your player's intent and approach, you can then decide if it succeeds, fails, or has an uncertain outcome and thus calls for a roll. In that latter case, assign a DC based on how hard achieving their goal is given their approach. Then roll to find out what happens.
Ranger: I want to try and tame the owlbear and make it a mount.
DM: Okay. [Paraphrases the Monster Manual to present a complication.] Although they are more intelligent than most animals, owlbears are difficult to tame. However, with enough time, food, and luck, you can train an owlbear to recognize you as a master. How do you go about trying to tame it?
Ranger: I will bring food to the area where it lairs every day at sunset and leave it. I make it a point to let it see me leave food for it. I will linger in the area while it eats as long as it allows me to until it no longer sees me as a threat. That should cover time and food?
DM: So it sounds like this will take days or weeks to happen. If you're willing to spend downtime days on this effort, you can make a DC 20 Wisdom (Animal Handling) check. If you succeed, it will no longer see you as a threat in 2d6 days. If you fail, it takes 4d6 days instead. That's the luck bit.
Ranger: And after that I can start training it as a mount?
DM: Yes, it will see you as a non-threatening source of food and will follow you around. After that, you can tell me how to approach training it as a mount and we'll see how it goes.
Ranger: Okay, cool...
Wizard: I will help him in this effort. If an owlbear will be following us around, I want to get on its good side at the outset...
DM: So it sounds like you'll be making that check with advantage once the wizard tells me how he actually helps.
Wizard: I create some minor illusions to lure the owlbear into the area where we're leaving the food and use prestidigitation to make us smell less appetizing than the food.
DM: Great. Go ahead and roll, Ranger... what are the rest of you doing during your downtime?
Welcome.
The simplest task resolution is to ask for an ability check and assign an appropriate difficulty class.
For instance. To tame an Owlbear, roll a Wisdom (Animal Handling) check vs a DC 20. If you succeed, the creature is tamed. If you fail, it will attack you.
Simple. And all you need to know to start.
For more fun, consider the obstacles and impediments that stand in the way of success. Opportunity, time, feed, etc. for each obstacle overcome, it becomes easier to tame.
For more on this concept, see DM 101 in my sig.
Thanks for the replys guys, great explanation from both of you much appreciated