This is by no means a high elo guide. I think Zyra can be really fun outside of lane and she can get some very good clear times with good pathing.

Your first clear is the most important because you'll most likely beat out the enemy jungler. You'll want Q start for the low cooldown to proc your passive plants lvl 1 and always position yourself towards the camp you'll go towards next to increase the chance of a passive plant spawning where you want them. Make sure you always attack the lowest health creep to reset your W cooldown. Get a feel for when your plants can kill the creeps by themselves so you can walk away while they slowly suffer and die and with some practice you should be able to consistently get a clear around 3 minutes (sometimes faster if you minmax your spawns well enough to kill 2 campst at a time) which lets you roam into lane for gank pressure before taking the first scuttle or to set up plants for the scuttle to take it on spawn. You can also put out good pressure to the enemy jungle as you shouldn't need to take much damage on first clear. Red, Blue and Gromp all attack your plant slow enough for it to time out by the time its ready to die. Wolves and raptors can kill it quickly but taking some hits while your plants are in the backline loses you very little health.

With good plant timings and placement you can solo most drakes and rift herald. Hextech drake will AOE your plants so only plant one at a time. Cloud drake attacks too fast for your plants to live so try and get help with it but the other 3 will usually kill a plant by the time your passive is back up or your W is available.

By the time you have Liandry's your clear should be fast enough to just walk past camps with 3 plants down.

Always stay back / behind terrain with vision past it to throw your E > W > Q > W to catch enemies off guard. Or when ganking try to predict with your E, it has a reasonably long range. If your E doesn't connect don't waste a W charge as they'll likely get away unless you can pop Q > W for some slowing poke. Only use a W charge for your E if it's going to land.

Keep an eye on your passive timer when you're walking through jungle as you can pause it by going into a bush to set it up nicer for a camp or to stall it for an ambush kill though beware that it still spawns randomly and takes a moment to pop out after you leave the bush.

Once you're hitting 3rd item you should be able to just sit behind your team or engage from a distance with E if the enemy has no hard engage or mobility like Akali to delete you. Your CC will set your team up nicely and your full combo of E > W > R > Q > W in quick succession which gives a root and knockup and some susbtantial damage.