Rek'sai is ULTRA useless outside the jungle and can't contribute meaningfully til you have a finished jungle item, lvl 2 boots, and a damage item. This will be about lvl 9 or so.

Reks only real contribution in the first 15 minutes of a match is to harass and poke at lanes.

You will not win any 1v1s whilst jungling. Your only contribution is to pick off stragglers in lane, or to join team fights, and this pretty much only occurs in bot lane.

Trying to carry with Rek is a bad, bad idea. Stick to your jungle and visit lanes that have aggressive enemies in them.

Rek'sai snowballs like crazy, so don't feed and let your ADCs get kills. When possible, play so as many of your teammates as possible get assists on kills.

tl;dr AVOID FIGHTING UNLESS IT'S IN A LANE and A NUMBERS SUPERIORITY. You will lose if you don't have the aforementioned items.

PROS

Is Mobile; bE is an amazing escape
Mobility is increased by crafty placements of tunnels
Can escape almost any situation
Ganking potential (after lvl 4) is ultra-high
Can duel tanks and can burst down squishies such as mages
Tunnels give a notice when enemies are near, as a destroyed tunnel indicates someone was there.
Better than average Jungle clear speed

CONS

Reqs MANY button pushing
Buttons pushing Reqs patience and MUCH practice
Doesn't do much outside the jungle til BOTH Jungle item and an AD item are completed
Like many AD-types, is susceptible to being focused
Reqs a completed jungle item VERY quickly into the game to deal any significant damage, and even then requires a completed AD item to be effective - doesn't have much to do first 4 levels except be ultra-cautious

Rek'Sai is a pure fighter, dealing massive amounts of damage very fast. In order to maximize the dmg output of this champ, you'll be pressing a LOT of button, and I mean a LOT. Her Q hits the target in front of her, and her tail has a lashing effect that hits behind. It's tricky to position, but is similar to Malphites E. So, when laning, make sure to group up wave minions. Rek'Sai has the same number of basic ability keys are everyone else, the default Q, W, E. But Rek'Sai can Burrow, which changes the abilities you can use. We'll refer to these as unburrowed, or u, so uQ, uW, uE. Burrowed as bQ, bW, bE. Abilities that are attacks, i.e., uQ, bW, uE, generate Fury, upon hit, per unit hit. Auto-attacking also generates Fury.

Rek'Sai has two basic passives. One is a secondary form of vision, granted automatically while burrowed. You are shrouded in the fog of war, so this passive is how you "see" things. It only reveals units that are moving, but it reveals them all, in a wide swath of the area around you in the form of circles drawn on the ground to indicate where they are, and if you pay enough attention, where they are headed. So, any stealthed Shaco, Twitch, or Evelyn, or a Wukong is circled. You won't see their unit character, only the circle. Minions and smaller jungle creeps are small circles; enemy champs and the larger jungle monsters (Gromp, mama Wraith, daddy wolf, big Golem, Red and Blue buff) are larger circles. The faster the unit is moving, the faster the circles are re-drawn. However, if the unit comes into either your or any ally/wards field-of-vision you still have actual vision per normal. Remember, minions run a defined path, and won't deviate til they come into contact with an enemy of theirs; you can use this to know, along with the size of the circle, what is moving.

The second passive is Fury of the Xer'Sai. This passive has two separate functions. Rek's abilities have no cost whatsoever, merely a cooldown. While burrowed, you use up fury to regen health. You have 100 fury points max, and use up exactly twenty (20) per second (so, 5 ticks max) while still burrowed to regain health. While the passive is active, i.e., while you have fury to use to regen, your next ability that generates fury will generate a bonus 15 fury. You can then guesstimate how to burrow and unburrow to regen health. It's too complex to do in team fights, I only ever do it while fighting Gromp. This is one of Reks main awesomeness characteristics. An uE at max fury does true, meaning un-mitigatable, damage. You must practice using only one or two stacks of fury for health-regen, so that it is super easy to get your true-damage uE Bite in (by getting it back to 100% quickly).

Rek'Sai is an attack damage jungler. But her bQ scales nicely off of ability power. However, there is only one item that both adds ability power and that also either adds attack damage or helps you survive in sufficient dosages that it warrants building AP at all. The bQ does enough damage to minion waves as-is, and the poking ability is enough to keep lower-health champs at bay. Although bQ damages the first enemy hit (then applies it's AOE component), stealthed units hit by either component of bQ are NOT revealed. So, PAY ATTENTION - if the blast ends prematurely, you can then be assured you have hit a stealthed unit.

You'll be building your jungler item first, then AD components, then boots.

Rek'Sai is an Attack Damage jungler. Her bQ scales nicely as a long-range Nidalee-type poke, but is AP scaled, so we won't rely on this for damage. However, you will be able to use bQ to get long-range kills on units at 14-15% health or lower (pretty much this will always be units that are turret-hugging, so make sure to check areas that look like a low-health individual might be hanging out at) and also to illuminate an area that has larger circles in it. A few tricks here - if you are in the Wraith camp, (the camp that gives Razor Sharp) your bQ will hit anyone turret-hugging. You'll be picking up a few easy kills this way, every day. Also, if you have tunnels set up nicely, you can poke with bQ, then scuttle through two (or MORE!) sets of tunnels to completely throw off the enemy.

If you don't like to invade, or yoloqueue won't help, then you start own Gromp, then Blue, wolves, and wraiths and back. In this scenario, use Smite when it can kill Blue buff (450 health).

If you don't like invading, I would suggest practicing in team-builder. Rek with a kill/assist lvl one is easily the best way to snowball.

I suggest always invading the map-bottom enemy buff; when blue, invade Red, when red invade Blue. If you invade enemy Red, then save Smite for the Golems. Smite the big one, attack the little one first. If you take enemy Blue, get out after you Smite it to regain health. This will be the only time you use Smite on anything other than Gromp (the single fat dude next to Blue buff). Gromps' Smite buff deals poison damage to an enemy unit that hits you with a basic attack. Smiting momma Wraith gives you "Razor Sharp", this buff does two things: first, it alerts you if you've been spotted by an enemy ward, and second it grants magical sight, granting knowledge of a ward in your vision area - Magical sight shows you all wards that are in the bush you are currently in and all wards that aren't in a bush. So, if you want reveal a ward that you think is in a bush, you must walk into that bush to check. It has two cooldowns, one that last til you see your first ward, and another, a much shorter CD that begins once you have been alerted that you have been spotted by a nearby enemy ward.

When holding back smite to use on momma Wraith, use it to deal the final blow, as the first CD doesn't begin til you use smite. I almost always rely on Sweeping Lens, but you might not. I find the bonus damage from Gromp too good.

An invade order goes like this, tRed > tGolems > own Gromp, own Wolves, own Blue, and back. Or own Blue (make sure you get a massive leash, to save smite for Gromp), own Gromp, own wolves, then check a lane, and try to begin your counter-jungling. Remember to prioritize ganking lanes that your team has pre-warded, and has an over-extending, aggressive enemy, esp a singleton (the support has backed to buy).

You can do Dragon at lvl 4 with the remaining Red buff, Gromp's buff, and blue, assuming you get a leash. Ping as you run to Dragon. Pressing the TAB key lets you know spawn timers for all buffs your team witnessed get taken.

Smite preference is always an enemy carry. If it just came off CD and you are jungling the order is Gromp > momma Wraith > Golem > Wolves

Rek'Sai is a playable champ due to the tunnels.

Therefore, when you are jungling it's imperative to place tunnels when not being pressured.

The trick, of course, is to have it, meaning bE, ready once the cooldown is up if you are caught out, or need to gap-close to secure a KILL. There is an indicator above the ability-bar, that tells you if you can set a new tunnel. Once you unburrow, uW goes on cooldown, meaning you can't set a new tunnel. So plan ahead.

There is tremendous skill involved in placing these. Competent enemies will constantly be searching out your tunnels. You should have one going from a bush > Dragon, a set near dragon in case they take out your Dragon-direct, from a bush > Baron, and one that is protected by a turret. This does not mean these are the only places you set them; you want to have 6 sets of tunnels up at all times.

The more sets of tunnels you have up at any given time will allow you to:

a) have more escape/gank potential

b) use ult from base (mostly) to secure kills/take objectives/ steal Baron

c) give the enemy a sense of accomplishment that they have rooted-out ALL the tunnels, so they give up looking

You're going to want to take IAS runes, and take magic resist as well. You want to minimize any poking magic damage you take, since well-placed tunnels will help you not take physical melee damage. Yes, there are ADCs who can poke from great distance, but the magic resist runes, I feel, are just better. You can easily add more MR runes, if you feel the need.