Arbitration/Steel Path build has different mods but same polarities, while this guide covers most of the game, including sorties and ESO, and the process of adding forma while playing the game instead of grinding in the latest affinity cave.
First time [Saryn]? Here's how to play: press 1(spore) at the enemy, then kill him with your weapon, now every other enemy in range has a spore.
If you have 3rd ability (toxic lash) active, it's enough to just hit an enemy to spread spores, and you get a toxin damage buff.
4th ability (miasma) scales with spores, aoe dot etc and so on, use against large groups for maximum satisfaction.
2nd ability - creates decoy, removes debuffs and speeds you up, the best skill you'll consistently forget to use, and the one that Helminth drools to replace.
Once [Venom Dose] is installed, hold 1 to buff weapons for everyone in range (including yourself) with corrosive damage. By default (rank 1 [Saryn] w/o str mods) it adds 100% corrosive damage (more than a standard elemental mod) for everyone in range. In comparison, Toxic Lash(3) adds 30% toxin to guns or 60% to melee for a max rank [Saryn], and only works on you.
Part 1 - no forma, no reactor, no exilus required:
Any maxed aura you can fit, just for the capacity.
[Stretch] and/or [Augur Reach] - range is cheapest and most important stat, and [Saryn] has a polarity for one of them out of the box, the other one should be added in free slot as you rank her up. (if you actually get/buy it)
Standard [Vitality] - also has the polarity, and it's priceless while ranking up (rank 6 or 8 is a good place to stop upgrading it)
[Cunning Drift] (not in exilus slot) and/or [Intensify] - [Saryn Prime] gets free polarity for this, but it's not as important. Either way, you already have a functional [Saryn] even without any levels.
Part 2 - make sure you have [Saryn Prime] if you don't want to waste reactor/forma:
Install reactor immediately, and forma/exilus/lens whenever you need them.
Arcanes are optional, [Guardian] is just useful for majority of frames by default.
[Venom Dose] - use first forma for this, and don't forget to activate it in game.
After using each forma, use [Venom Dose], [Vitality] and [Stretch] as a core, it should fit for any MR. Add [Intensify] in free polarity if you have capacity left.
Second forma - [Augur Reach].
Third forma - [Cunning Drift] in exilus.
Optional: forma aura (ideally with aura forma), and umbral forma.
Optional: Use [Augur Reach] instead of efficiency if you really want some extra range (ESO).
You're done. Look at the build and just copy the mods or switch over to Arbitration/Steel Path build.
A certain spoiler ability from a quest takes care of all energy in this build, I don't know what you're doing if you don't have it by this point.
[Corrosive Projection] - spores don't strip armor faster than enemies die + corrosive is now capped at 10(80%) anyway, so this is still the best aura for starting out.
After getting a Helminth ability, [Growing Power] becomes best default aura.
Neither are matching with original polarity, and you can't go wrong with installing an AURA FORMA.
Helminth Ability - [Rhino]'s Roar, it just has too much synergy. By this point I recommend [Growing Power] for aura, and switching to [Corrosive Projection] when enemies are immune to viral procs (Cambion Drift)