Sorry, no experience with breeding these. I understand though, that most gouramis can be bred in the same way. I copied this once from Sylvia:
I breed pearl gouramies on a fairly regular basis (and have bred several other species - including three-spots). Actualy, three-spots are on of the easiest (if not the easiest) to spawn so they are a good one to start with. The major downside is their size and potential for aggression.
The first thing you'll need - as you know - is a breeding tank. Something at least 10 gallons is necessary but the bigger it is, the longer you'll be able to raise the fry without worrying about grow-out tanks or water changes. Note, BTW, that this is an important consideration - three-spots (even their fry) are quite hardy and they'll produce hundreds of eggs - what will you do with all those fry? I should say that it's rare that someone gets many more than 10-20 the first time they try to spawn gouramies as mortality rates can be high - but even this number is quite large - will you give them to your LFS? Will you have adequate grow-out space?
The size tank I'd suggest personaly is a 20 gallon but only half-fill it. It's the surface area that's most important for the adults and the water level should be low if you want to maximise the number of fry that survive and if you want to make sure the male retrieves all sunken eggs while spawning. Later you'll have to fill it up so that the fry aren't over-crowded.
What I tend to use for breeding is a large plastic storage box. Anything at all, provided it's food-safe, will work. The big upside is that this is extremely cheap and you can get as large a volume as you like. The downside is that you cannot see through the sides clearly (most are at least partly opague). This is only realy a problem if something goes wrong though. In fact, fi all things go well, opague sides are good as they make the breeding fish feel more relaxed. Avoid anything dark colored - white or light grey etc is best - this way you can see even tiny fry quite clearly from above.
In this tank put a sponge filter and heater and set the temperature to about 78-79 deg F - you may need to take that up to 82 to get the fish to spawn but this is usualy unecessary with three-spots. Add, also, a ceramic pot or similarly simple cave-like ornament (this is for the female) and either some floating plants that you can easily remove or a styrofoam cup cut lengthways (browse the betta forum FAQs on breeding - there must be something about this there). These floating things are to provide the male's nest with support. Once the fry are free-swimming, it's best to remove all objects - this'll make monitoring them easier and they'll be able to get hold of food easier as well.
A light isn't necessary but the room the breeding tank/container is in should be relatively bright. This'll ensure the fry can see their food and will also mean the male has an easier time of caring for the nest.
Cycle the tank fishless (I skip this step by running the sponge filter I'm planning to use in an established tank for a couple of weeks beforehand). Then perform a large water change with dechlorinated water - you need to remove all of it so the water's as fresh as possible. This'll reduce the number of water changes you need with the newly hatched fry in the tank.
You can put the female in for a week or so and, during this time, condition both the female and male with as many live and frozen foods - and the occasional veggie - as possible. If the female is looking gravid and both are healthy, you can try introducing the male. take care to acclimatise fish when you move them from one tank to another - the temperature will probably be different for one. You can put the male in a plastic bag as you'd get him from an LFS for this - this is also a chance to see how the female reacts and whether the male looks interested. Many a fight can be avoided by watching how they react to each otehr's presence this way.
Then you just put them together and hope for the best
Once the male and female have spawned (you'll see the male rap around the female and she'll release eggs which he'll fertilise and ensure are in the nest), the male will usualy become quite aggressive towards the female. Even if he doesn't, she can be returned to the main tank - no need to keep her in the breeding tank and she deserves a rest. A couple of days (at most) later, the eggs will have hatched and the fry will be free-swimming. In the meantime, don't bother feeding the male. Most of mine won't eat during this time anyway and it's best to avoid 'polluting' the water.
Anyway, with the fry free-swimming, it's time to remove the male and start feeding. This is where it's important that you've prepaired some kind of miniscule live food. I tend to use microworms but baby brine shrimp or vinegar eels are good too. The real issue here is that you must eb prepaired a good few weeks before spawning (less with the shrimp) or your fry could starve. in fact, at the very beginning, many fry can't even take these large foods and need infusoria (these are easy to culture). You can try liquid egg-layer foods of the commercialy sold type and follow the instructions - these actualy serve as good infusoria-food themselves so you can use it to culture them. As the fry grow they'll be able to take larger and larger foods- train them onto powdered flake (but feed them some live things also) as soon as possible. This'll make things easier both for you and their future owners but, mroe importantly, live foods are messier than flake.
Which is something else I should add - by now you'll filled the tank right to the top if it wasn't full already and you'll have to start doing some partial water changes. What I do is syphon as I would any ordinary tank but all of the water goes into a white (or light-colored) bucket - this way you can see the fry you've sucked up (and you almost inevitably will suck some up ) and return them safely to the tank. Make sure the water you use to replace that which you've removed has the same chemistry - including temp. - or you risk killing all the fry.
That's basicaly it, I think . For info. on live foods, check out the pinned topics in the betta section - they have some stuff on culturing foods. Also, search this forum for more gourami breeding threads - I know there are quite a few - as well as the betta section seeing as bettas are just another gourami species and are pretty much the same to breed (+ jars).
Have fun
