There are many Rek'Sai guides on how to play her, how to climb elo etc, but the main thing with playing every champion is maximising it's mechanical potential by fully understanding every ability of a champion. Therefore, for full guides please visit other ones - I will skip it and share with you some mechanical tricks you need to learn in order to play her to her full potential.

1. Basic attack resets - before using your Q for jungle clearing or ganking, ALWAYSuse auto attack first and then immediately click Q to reset your auto attack. It will not only deal more damage, but will let you have 4 attacks of Hail of blades (instead of 3) and will also generate your Fury faster.
2. Use your passive to regenerate health in jungle - after releasing your full combo on a jungle camp (Q when borrowed, then unborrow (W), then auto attack and then 3 basic attacks with Q, you should press W to burrow yourself and regenerate health while moving away from the camp towards the next camp. This will not make you waste time, as you would have to move anyway, but in the meantime you will regenerate some health.
3. Rek'Sai's E (tunnel) has higher range than flash - use it to your advantage to gank from positions where other junglers cannot (for example tribush on bot or top, Raptor's camp on mid, the bush near blue buff on Bot side of the map etc)
4. Tremor Sense senses only moving champions, therefore you have to pay attention even if you don't see anything detected. But you can predict where someone stands if the 'circle' stopped moving within your area - use this to your advantage
5. Remember to use your E only with full fury to deal true damage - otherwise the skill is pretty useless, as it deals low damage
6. Rek'sai's R makes the chamapion untargettable, but not immortal and that is different. You can dodge some abilities like Caitlyn's ult, Karthus' ult or fizz' ult, but you cannot 'dodge' damage over time abilities, like Ignite, Malzahar's E, Cassio's Q or Singed's Q. Simply press R when Karthus ults and you will not receive any damage.
7. Rek'sai's tunneling can be interrupted by displacement CC ONLY. It means that if you pressed your tunnel and you started entering it, stunning you will not stop you from entering the tunnel, but if Alistar headbutts you in the face while tunneling, you will be displaced from the tunnel and the channel will not finish. Use it to escape or engage effectively, as Rek'Sai's tunneling is 'immune' to some kind of cc.
8. During gank, you can unburrow yourself and start spamming auto attacks on the enemy champion to 'shorten' the animation of unburrowing. It means that you can start attacking the enemy champion before the animation of unburrowing is ended. Remember to use this trick during ganking to maximize your burst damage.
9. You can R enemy champions that have been damaged by you in the last 5 seconds. It means that you can ult a champion that you have just blue smited - remember it while playing against heavy mobile champions like vayne or kalista, which can be hard to damage otherwise.
10. You can also knock up enemies while entering your tunnel - it's pretty hard to master as it has to be timed perfectly, but it might be useful sometimes. When you clicked a tunnel to escape while burrowed, you can press W immediately after entering the tunnel - you will both knock the champion up and deal damage and finish the channel through the tunnel.
11. Remember that your Q reveals champions hit that are not stealthed. It means that if you have an enemy champion with stealth (like twitch) hitting it with Q doesn't reveal that champion, but will deal damage anyway. Q reveals monster camps and epic monsters aswell. You can use it to see the drake or baron's HP to try a sneaky steal.
12. Keep in mind that unborrowing (W) is a displacement CC. It means that you can stop in-air enemies from performing their abilities, for example Zac's E, lee sin's Q, Jarvan IV's EQ combo, tristana's jump etc. There is a possibility for a huge outplay by cancelling key engage tools by enemies. You can stop above abilities without incurring their damage or CC they provide - if Zac jumps on your team, you can unborrow while under him to disrupt his jump (you will not receive any damage nor CC). Same thing with lee sin's Q - if lee is flying towards you with his second cast Q and you time the unburrowing correctly - you will knock him up without receiving his Q damage. Use it to negate enemy team's engage potential.

Thank you