There was a pretty decent DIY on this forum - for a 2001 Chevy Prism, but the work is essentially identical for all 1ZZ-FE engines.
https://www.corolland.com/forums/index.php?/topic/23007-1zz-fe-timing-chain-tensioner-diy/
Dom's right - usually the tensioner is fine, just the o-ring shrunk, causing it to leak. If you have a difficult time finding the right o-ring or don't feel the tensioner looks right - just replace the tensioner. From the dealership + o-ring, set me back about $28. Many have been able to get that even cheaper.
You don't have to remove the valvecover - though usually, when the tensioner starts leaking (most after 100K miles) - might be worthwhile to remove the valvecover and replace the grommets and o-ring around there as well. The valvecover may not be leaking yet - but since you are right there, might as well change them. Allow gives you access to check valve clearances - let you access the condition of the the end of the engine as well.
Replacing the tensioner is pretty much plug and play - the only tricky part is getting the tensioner to release the plunger from the "hook". Once you look at some pictures of the tensioner, you'll understand. Having the valvecover off - you can visually see the plunger release as well as hear it snap in position.
If you feel uncomfortable in removing the valvecover - you can easily do this with the valvecover in place - just have to wiggle the crankshaft back and forth to dislodge the hook and listen for the popping noise.
As for timing chain lifespan - as long as you stay on top of the maintenance - should last the life of the car. There is no set replacement interval on the chain - just audible checks. Note that this is an interference engine - so when it lets go, valve damage is very likely. Should you be worried - nope - just change the oil on regular intervals and note any unusual or excessive chain noise. Proactively replacing the chain is no guarantee that you will avoid chain breakage. Could be a sprocket that loses teeth, or the chain guides wearing out and eating the chain, timing chain tensioner could get stuck and wear out the chain or put too much slack in it. Once the engine gets up to 200K or 250K miles - then I'd say it be worthwhile to tear into it and see if the chain is overly stretched out. Remember that there have been a number of 300K+ mile Corollas with the original chain still on there. I wouldn't worry too much about the chain.