When the game starts, your first order of business is to explore the galaxy around you, and try to find systems with 5 planets (or 4 planets if they have resources you really need). Ignore anything with less than 4 planets, and don’t pay too much attention on all the FIDSI bonuses of the different planets. With Vodyani, the only things that really matter is the number of planets (your population have a +8 of everything, so it’s always better to have more population, than better bonuses).

So send your Wheel and your Leecher around, making ample use of your Wheel’s probes (don’t waste them on anomalies yet), to unveil the map around you.
Try to avoid pirates, and if you encounter any, just flee.

In the meantime, slowly build your main system (starting with Cerebral Reality etc) with what you have available. Don’t waste production on food-only infrastructures.
As soon as you have around 500 credit accumulated, go to the fleet screen, and edit your ark. Change every single slot that can host a module, and put a “All Must Provide” in it.
Then pay to upgrade your main ark to the new design.
Since your population is so powerful at generating all FIDSI, and Essence is needed to increase your population, it’s better to focus all your arks on generating only Essence, which in turn will raise your population faster, and in turn will generate LOTS of science/dust/production/influence.
Also, the Arks are powerful enough to provide all the essence you need, so you don’t really need to bother with leeching minor/major factions.
(remember to keep upgrading all the Arks in the future when you unlock more slots, or “All Must Provide II” etc).

Also, look from the first turn, which luxury resource is needed to Boost your population (it’s chosen at random at the beginning of each game). Then quickly find a system that has this resource, and make it your first priority to send an ark there (or maybe even move your existing Ark there).
If you don’t see any system with this resource, then make it a priority to research Galactic Commodities, then buy all of it from the market, whenever there are some available.
Since all your resources come from your population, keeping your population in constant boost (generating +8 instead of +4) should be a top priority.

In the first few turns, spend your essence to raise your main system to 3 population.
This should give you enough time to identify a nice 5-planet system and get the science needed to colonize some of its planets.
When that’s the case, accumulate your essence until you max it out.
(most likely, you will have built everything you can build at this point, especially since you’re focusing the research on making planet habitable, not on getting things to build, but it’s ok. Just have your production to generate essence from dust).
Once you maxed out your essence, produce an Ark, and send it to the 5-planet system you want to colonize.
TIP: one useful “cheat” here, is to change the design of arks before you produce it, and replace the All Must Provide by speed engine. Then produce an ark, move it (most likely in 1 turn with all those engines) to the new system, anchor it, edit the design again and put back the All Must Provide, and upgrade your new ark to the original design.

When you want to remove those pesky pirate bases, or if you found a perfect-looking 5-planets system already colonized by a rival faction, you’ll need to attack.
But you probably noticed that your manpower is very very low. That’s normal for vodyani (since they don’t rely on food).
So before going to war, you’ll want to research Autonomous Construction, to have access to Titanium A2S Slugs modules.
As soon as you have it, open the fleet designer and edit the Leecher. Replace all the modules with Titanium A2S Slugs.
This way, a single leecher will reduce the manpower of any enemy system by 60/turn. So a small (and very cheap to produce) stack of 5 leechers will empty any 300 population system in just one turn.
Then send some armed ships to defeat the enemy’s ships, and as soon as the system is defenseless, send your 5 leechers, make them stay one turn, and next turn just bombard the system out of existence, no matter how few manpower your ships have.

At the beginning, your systems are maxed out at 3 population per planet.
In order to raise this limit, you will need to apply System Development (in the Economic screen) to each Ark.
Unlike other races, the System Development for Vodyani is not only about applying a small bonus, it’s needed to raise the population cap (which as you understood by now, is MUCH more important than the small bonus).
So, do not set up the upgrades using a luxury resource that gives a bonus you like. Use the resources that you are producing in the biggest quantity.
It’s very important that you are able to upgrade all your Arks (and you’ll quickly reach 8 or 11 Arks).

Once you will have established 8 or 11 Arks, all of them maxed out in population, and you’re almost out of things to build in each Arks, it’s time to wrap up the game, and choose how you’d like to win.
The fastest by this point, is probably to go for a science win. Just edit your ark design, and replace all the All Must Provide by All Must Study. Then upgrade all your arks.
You’re now putting the Sophons to shame, and should finish a science victory in a dozen turns.
Or, replace by All Must Tithe for an economic victory, or All Must Serve for a wonder victory, All Must Worship for alliance, etc.

If you’re doing everything right, you should consistently win before turn 100 when playing the Vodyani.
Have fun playing.