It's when you have the gouramis in a tank of their own that you have to take the female out if you want to get the eggs to hatch and raise the fry. In a community tank there is no point taking her out as the other fish will eat the eggs before they can hatch. The male will try to chase them away but there will be just too many fish for him to chase off - while he's chasing one fish, another will sneak in.
Gouramis come from water that is a bit stagnant. That's why they evolved to have a labyrinth organ, stagnant water doesn't have as much oxygen as nice clean water so they had to be able to use air to get enough oxygen. The labyrinth organ is a system of hollow bones in the head, they gulp air into this organ then they can get oxygen from it. Even though our tanks have lots of oxygen in the water they can't not gulp air and if you put them in a bag of water and don't leave an air space in the bag, they can actually drown!
Because of the stagnant water, the eggs have to develop near the surface so they get plenty of oxygen too. So males blow bubbles which they coat with something to make them sticky and they clump together. He is the one that makes the bubble nest, then when they spawn they wrap round each other, she lays the eggs and he fertilises them. They are both in a stupor for a few seconds, then he comes out of it first and dashes round sucking the eggs into his mouth and spitting them into the bubbles. They do this several times till the male decides there are enough eggs. Then he'll chase the female away and any other fish that comes near. It is his job to guard the eggs and to catch any that fall out and put them back in the bubbles. If they are in a breeding tank, you take the female out as soon as they've finished laying eggs as breeding tanks are usually small and he might kill or injure her if there isn't enough room for her to get away from the male.
After a few days the eggs hatch but the fry can't swim at first. They hang from the nest with their tails sticking down, and the male makes sure they don't fall out. After a few more days, the fry start to swim and leave the bubble nest, and if they have managed to make it this far they'll get eaten pretty quickly. If they are in a breeding tank, once the fry start to swim you have to take the male out too or he will probably eat them himself.
You have to look very carefully at the bubble nest to see the eggs. The bubbles are see though and the eggs are white-ish and not see though in between the bubbles. They are quite hard to see, I usually have to get a magnifying glass to see them properly. The eggs hatch in 2 or 3 days, and it's a week after the eggs were laid before the fry start swimming. They are very tiny, there is a pic in post 5
here . By the time I found the fry, they were able to swim and the bubble nest had gone. They'd all been eaten by the next day.
Some people have managed to use a breeding net. They put a piece of glass or plastic under the bubbles and carefully slide the bubbles and eggs onto it, then slide them off in the net. There are some problems with this. The eggs and newly hatched fry can fall out of the bubbles but a net is too small to put the male in as well, so there is nothing to put the eggs and fry back. And I have found that gouramis are very good at sucking eggs and fry through net, so any that fall to the bottom will be sucked though and eaten.
Then there's the problem with getting them to grow. I have never managed to keep fry alive more than a couple for weeks. They don't have a labyrinth organ at first, it has to grow and while it's growing the fry have to be kept warm and with very moist air on top of the water. Any colder air getting in will kill the fry, and it is very difficult to feed the fish and do water changes without letting cold air in to the top of the breeding net.