The first ability for +1 loyalty allows you to draw a card and then add one mana of any color to your mana pool. That's an ability that will provide advantage for any deck. It's an effect similar to an older card called Explore, which saw a ton of Standard play, except that let you play an additional land during that turn. Getting one mana of any color instantly added to your mana pool can in some ways be better. (Say you don't have any land to play, for example.) In any case, it's very similar advantage.
The second ability for -2 loyalty creates a 4/4 red Dragon creature token with flying into play. This allows Sarkhan to pass the ever-so-important "can he protect himself" test for planeswalkers. Even if all you do is make 2 4/4 Dragon tokens with him, he's been worth it.
The ultimate ability isn't necessarily one that will see much play in ordinary Constructed, but you never know. You get to search your deck for any number of Dragons and put them right onto the battlefield. This "super" Dragonstorm effect could be relevant if Dragons simply overwhelm Standard, but mostly it will only ever see use in Intet, the Dreamer or Scion of the Ur-Dragon Commander decks.
Truthfully, most planeswalkers are played on the strength of their first two abilities, and Sarkhan's are both excellent for Constructed purposes. Temur Tempo decks in the current Standard will make room for him and current Red/Green Devotion decks will probably splash Blue mana for his benefit - although they already have Sylvan Caryatid at the moment to fix for that. He's definitely going to see Standard play, but the five-mana casting cost may make him tricky, though not impossible, for Modern. His Commander prospects are a bit limited due to the three colors in his casting cost, but he'll certainly see play where he can.