I’ve just switched to tubeless so this is a forward looking question.
I’ve been told that I should replace the sealant every 3 months.
My question is, do I/should I take the tire off to clean out old sealant first?
Or do I just leave it on an pour in new sealant?
No need to unless you REALLY want to save a little bit of weight from the old sealant remaining in there. Personally, it’s not something I bother to do.
You can just leave the old stuff in there and pour in some new sealant. You can even take the valve core out of the valve and use a syringe to insert the fresh sealant that way. Then you don’t have to take the tire off at all!
Do what you want with the old, I leave it but do read the label on the sealant.
For example, Regular Stans can be injected with their syringe, Race is chunkier and can’t.
Ask me how I know! 
As above I’ve never bothered cleaning out old sealant. My personal experience is that if you don’t have any punctures then sealant lasts a lot longer than 3 months before needing to top up. I’ve regularly gone 6+ months and still had plenty in there. Suspect this varies quite a lot with conditions though, I’m in the UK and bikes are stored in a garage that stays pretty cool so they’re spending little or no time at high temperature.
Personally I’ve had poor experiences injecting through the valve. It’s a messy process, quite often ends up with sealant everywhere if it clogs up, and increases the chances of my valves getting blocked up. I find it much easier to just pop one bead off for maybe a third of the wheel diameter and then pour the sealant in. Also means you can see exactly how much sealant is left in there. And minimises the chances of bigger lumps in the sealant getting filtered out by syringe, tube or valve, so anecdotally my sealant seems to seal more holes than when I was injecting it.
Sealant explosion in your living room after attempting to forcefully inject sealant through the valve anyway? (Don’t ask me why I made that guess…)
@trebor leave the old sealant, it helps seal punctures
I personally take the valve core off as well and insert the sealant through there. It’s quick and easy and messy-free (for me). Popping a bead off takes more time and can get messier (for me).
You can try both techniques and see what works for you. Just make sure to turn the wheel after you apply the sealant if you’re popping the bead so that when you place the tire back the sealant is at the bottom and the popped bead up top; this way sealant won’t go everywhere, haha. And if you’re inserting through the valve core make sure it’s at the bottom so you get a vertical position when inserting the sealant.
Some sealant cannot be injected through the valve core - Stan’s Race and I think Silca come to mind. But for the most part, you’re not using those for every day riding.
Pop the bead on one side, pour some in.
I do like to fully remove the tire and clean them out once a year personally if the tire doesn’t get replaced by then.
Personally - save yourself the hassle and use Orange Seal Endurance or Stan’s for Every Day riding. Orange Seal Regular or Stan’s Race if you have an event coming up and you want sealant with the best sealing capability / flat protection. Stan’s race sealing the better of those two.
Yeah, just top it up when you get nervous about how long it’s been. I use Stan’s and always inject it through the valve stem (with the core out), it’s far less messy in my experience than trying to seat a tyre with sealant in. I use a syringe with a bit of tubing that goes through the valve stem, so there is very little mess. Put the valve at about 4 or 8 o’ clock, so that the sealant can run into the tyre and not stay near the valve.
If I take the tyre off for any reason, I wipe the old sealant up and add new stuff. (It does seal better when its fresh and not about a year old 
)
Stan’s Race has ‘bits’ which won’t fit down a core-less presta (or will block it) but they do have a top-up system that you can use to replenish every 3-4 months (depending on storage conditions) through the valve
No, just pop,of a bit of tyre bead. Add fresh sealant, put bead back and inflate. If you use presta with removable cores then you can inject that way. I don’t use presta but the newer design of high air flow valves. The later allowing easy reseating with standard pump.
I am relieved to hear I don’t need to take the tires off every 3 months 
That sounded a lot like having to fix a puncture regularly (although in less stressful circumstances ) 
Thanks to everyone who’s chimed in 
if you want an even easier tubeless-bikelife you can get the Reserve Fillmore Valves. 3 times the airflow of traditional presta valves and no valve core to become stuck. They are expensive but worth the upfront cost (imho).
No need to clean the tire interiors of dried latex. In particular, you might find previous punctures that had been sealed are leaking again and causing you problems now.
Generally I top-up the tire rather than trying to remove any existing liquid. I basically always inject through the valve stem with the valve core removed vs trying to pour it into the tire before fully seating the tire. Probably too often I’ve let the sealant dry out entirely and just keep riding on it for months.
If one is using something like a GP5000, this is nearly impossible without making a giant mess.
@trebor Get a good valve core removal tool. The cheap aluminum ones eventually get chewed up. The Stan’s one is my best one and good quality:
Also get a big syringe to inject through the valve core:
I think that cleaning out your tires defeats the purpose. The dried sealant forms a nice barrier against thorns and the like. I’d keep it plus it’s kind of a waste of time to clean out dried sealant that weighs next to nothing.
What I’ve started doing in this situation or when using sealants that can’t go through the valve is the following:
This has made difficult tires much easier to handle. I was able to deal with a pair of Corsa N.EXT with this, and those tires a terror.
I’ve been able to do this with both 32c GP5000 S TR, and AS TR. Most recently with S TR and Vittoria inserts, could have added Silca this way.
When the S TR was released I bought either 28c or 30c, and it was impossible to mount. Sold them. Completely different experience this year.
I’ve got 32 Corsa Nexts. 
they’ll be okay to do when I need to do this
Why?
The wasted time is subjective, but let’s be realistic - dried sealant is not forming any sort of a barrier against anything that’s already pierced the tire, it’s nowhere close to the strength of the rubber tire that’s already been pierced and way, way, way thinner. Maybe there’s an argument for dried particles and old sealant helping plug any future holes, but that’s it.
I don’t do it every time, but I still advocate for cleaning out once a year - mainly because I’ve often seen tires start to develop an imbalance and “pools” of sealant hardening in spots around the tire.
And, just because I’m OCD like that…
Once a year works for me 
I generally have to replace my tires annually anyways.