Sylas is a versatile jungler that you can pick every game and expect to have relevancy. He has decent clears, no clear weaknesses to early game jungler due to his inherently durable kit with healing and terrain scaling, and amazing ganks and counterganks due to absurd rundowns and 2v2 abilities.
His ultimate allows him to make guaranteed ganks towards certain lanes after 2/3 clears and he scales monstrously in a teamfight environment, and can also adapt to splitpush due to his waveclear passive.

Sylas is interesting in the jungle currently because he can take advantage of every meta clear path. You can Red->Krug->camp/skuttle if you wish to hit 3 and gank or vertical jungle, you can Red->3 raptors->wolf->blue for a quick lvl 3 on the opposite side of the map. You can Red->Lvl 2 gank to great success before taking skuttle and vertical jungling as well. Few junglers have his many options and are equally relevant doing all of them. It is up to matchup and lane priority for you to decide which would fit the game best.

After the game hits 10-12 min, Sylas has a different role on the team. He already has R (which is on a low cooldown) and if you have sheen you have greater ability to take towers than you already had. During this time you want to focus on taking all tier 1 towers, or if you can't then your goal would be to get vision around great objectives.

In late game you will either be teamfighting into comps that have good teamfighting ultimate abilities or splitpushing in scenarios where your team doesn't need to fight as a win condition.
If you are teamfighting then it is important to hijack ultimates in order of teamfight priority since your ult will be on a 9 sec cd by then. For example, if the enemy team is Sion, Sejuani, Xerath, Caitlyn, Alistar then you would poke with Xerath and Caitlyn ultimates first before engaging with a Sej/Sion ulti and using the Alistar ultimate mid fight for added survivability.

P: Be sure to weave in auto between abilities like you would on Riven. This maximizes DPS. Most commonly E->AA->Q->AA->E->AA->W->AA
Q: Your Q extends further than your other basic abilities, use it to chase down ganks and stragglers.
W: Use it when you or your opponent is below 40% hp. It cal heal and execute, but will do neither if you dont use it correctly.
E: Your E shield can be used to block important abilities for teammates and dodge abilities, while your E stun can be used to intercept certain abilities such as Lee Sin 2nd Q and Sion Q charge. You can dash in for ganks with your shield and proc red buff, wait out the E timer with Q until your enemy flashes and catch them with the stun and followup with W to complete the gank.
R: Don't be afraid to throw your ult around. It is incredibly low cd and champion ultimates are likely useful no matter what.