I actually main Rek'Sai. Here are some tips. It's long, but I promise it will help you.
-
Her clear is pretty decent speed, but the real pros of her clear is that she can end the clear with almost full health. Start Krugs, immediately smite for the Heavy Hands buff that stuns monsters. Then go to Raptors, and MAKE SURE you kill the little ones before the big one, they hurt almost as much but they die faster. Then, go for Red, and about 10 seconds into fighting Red, your Smite should be up again. Smite it, and you get your health back. Use your health potions as needed. If you're low after this clear, kill the Scuttle Crab and then burrow, the fury you gained will get some health back. Make sure that you knockup camps as much as possible to reduce damage, and try and go right underneath them to knock them up, because they are knocked up for longer. However, when the timer for the knockup is getting close to being ready, burrow, and BACK OFF FROM THE CAMP. The monsters will follow you, and you will be able to regain some health back from the fury you gained! Make sure you don't kite them too far back, or they will reset. Also, when using your Q, make sure to use it IMMEDIATELY AFTER an auto attack, as it resets your auto attack timer, maximizing your damage output in a shorter timeframe. Try not to use her E until your fury is full for maximum damage, as the cooldown is long enough that you can only really use it once per camp.
-
After this clear, you should be level 3, and at full health, or almost full health. Look for overextended enemy laners. Chances are, they won't expect such an early gank. Ping that you're coming, and hide in the bushes. When you're ready, tunnel all the way out into the middle of the lane behind your enemy, cutting off their escape route, get underneath them, and knock them up, use your Q, and use your E as LATE AS POSSIBLE, this will maximize damage. Optimally, you want max fury before using E, but sometimes they're getting away and you can't. You should either kill the enemy laner with the help of your teammate, or at LEAST blow a flash. Also, if you can't quite reach an enemy after tunneling into the lane, don't be afraid to flash RIGHT UNDERNEATH them to knock them up for the longer 1 second duration. This will help to secure the kill, instead of giving them a smaller knockup if you only get partly under them. If you're low after this, go back and buy a Stalker's Blade and maybe some boots and a Long Sword.
-
If no laners are overextended, keep clearing the jungle. Rek'Sai can clear the jungle 2 or 3 times without going back if you correctly fight camps, healing when you can, and knocking up when you can. Also, try and use your burrowed Q whenever you start a camp to get some extra AOE damage off, and also use it whenever you burrow for another knockup on the camp.
-
Rush a Hydra. I like to get Vampiric Sceptre first for the sustain in the Hydra build, and then get the Tiamat second. If you're ganking a lot though, try and get the Tiamat first, since it will increase your damage more. Leave your jungle item as Stalker's Blade for a while and rush Hydra and your damage will skyrocket. Gank at every opportunity. Use your tunnels to quickly block off your enemies escape routes when you gank. Bonus points if you tunnel through terrain and surprise them. If enemies are not overextending, try and get your teammates to bait them into pushing towards your tower. This will make ganks much easier. With the damage from Hydra, you and your teammates should be able to finish them off.
-
After Hydra, you probably want to build tanky. If the enemy team is AP heavy, or has fed AP members, I actually love to build a Hexdrinker into a Maw (though you don't have to rush the Maw and just stay at Hexdrinker for a while). The damage it gives is great but still provides good MR and an MR shield too. Spirit Visage is also great, increasing the lifesteal from Hydra and also increasing the heal you get when you burrow, allow you to leave teamfights, heal up, and then re-engage. If their team is auto-attack heavy, build Ninja Tabi and Thornmail. If they're reliant on attack speed, build Randuin's Omen, or just build Randuin's if they're AD casters, because the extra health will help. If you're really really fed, get Mobility Boots and a Bloodthirster after the Hydra, though generally these options are not the best. Black Cleaver is a great late game item if people start stacking armor, and your passive attack speed on your ultimate will help to shred their armor down fast. Whatever boots you build, I love to get the Furor enchantment. It really helps you stick to your enemies while auto attacking. Make sure to attack and then move after each auto attack. You don't want to build attack speed items, except maybe Blade of the Ruined King if your enemies are stacking health, since you already get it from your ultimate, and also your Q has great AD ratios on it, and you're missing out if you don't go for AD instead of attack speed.
-
After you have Hydra and some tanky items, its time to talk about your jungle item. Stalker's Blade is great for ganks, but in teamfights, it's less useful. If you're fed, stick with Stalker's Blade and upgrade to Warrior. This is great against stacked armor if Black Cleaver isn't enough, and you can also catch people with the chilling smite and then get under them to knock them up. If you're finding that you're having trouble 1v1ing a certain fed member of the enemy team, change your Stalker's Blade to a Skirmisher's Sabre before upgrading to Warrior. Why? Because this reduces their damage when you smite them, and increases the damage on your basic attacks to them. Chances are, you're not trying to catch them, they're trying to catch you, so turning around and killing them using challenging smite is great. Finally, the alternative to upgrading to the Warrior enchantment is getting Cinderhulk instead. This item is great if you've build a few items with health on them, like Randuin's and Spirit Visage, since the Cinderhulk grants an extra +25% bonus health, so it will maximise the health you got from those items.
-
Time to talk about runes and masteries. You want to go offensive masteries mostly, with a few defensive. Rek'Sai shines with early damage, and then late game tankiness, so make her early damage shine with offensive masteries. With runes, I like attack damage reds and attack speed quints for clear speed, armor yellows to reduce monster damage, and SCALING CDR BLUES. Why? Well hear me out. Most AP champs can be dealt with with an early Hexdrinker, so the MR isn't needed as much. Also, jungle monsters don't deal magic damage. Secondly, you get a huge amount of your damage from your abilities. Sure, you're an auto attacker, but you have amazing AD scaling on your Q. Having it off cooldown a lot is great and increases damage output. Also, you can use your E true damage execute more, tunnel more for more mobility, etc. You can also use your ult REALLY REALLY often late game with so much CDR, which is great for splitpushing and then rushing to teamfights when you are needed, or backdooring after dying really quickly (make sure to get homeguards if you're doing this, otherwise stick with Furor). However, I chose scaling instead of flat because you only need to use your abilities once when ganking, so you don't benefit from the CDR as much until teamfights, which are more late-game occurences than early. Also, you'll have blue buff a lot more early game for the CDR, whereas lategame you generally donate it to your AP midlaner. Full scaling CDR blues gives you 15% CDR at level 18. Add the Sorcery mastery and you get an extra 5%, equaling 20% at level 18. Then, combined with TWO any of the following items, which all give 10% CDR, you can get 40% CDR at level 18 and have insane DPS in teamfights, while also being tanky:
-Warrior Enchant Jungle Item
-Black Cleaver
-Spirit Visage
-Ohmwrecker (for late game tower splitpushing or tower diving if you feel like you need it)
Chances are, you're gonna be getting at least 2 of these items. Even if you don't and only get 1 it's fine, you'll probably be able to pick up blue buff, and 30% CDR is still great too.
Anyway, I hope this helped. Sorry it's long and kinda messily laid out. Ask any questions if you need to!