There are many ways to make money in Pocket Frogs. The methods include: selling frogs, racing frogs, and selling decorations.
Breeding and Selling Frogs: A consistent money-making method
Look for frog combinations that always result in a profit. For example, if you breed Glass Chroma Pompeius and Beige Chroma Pompeius, it will always result in Glass Chroma Pompeius.
Breed as many valuable frogs as you can, and decorate your habitats with decorations that increase happiness as much as possible. Move the frogs to a fully decorated habitat and wait for the frogs to reach adulthood and maximum happiness. You can use potions and trips to the pond to speed up the process.
After you sell the full grown and happy frogs, repeat the process to continue making a profit.
To guarantee that a frog pairing will be profitable, one of the frogs must be exactly 1/3 the maximum value of the other frog. This will guarantee that the breed cost won't be higher than the value of the least valuable frog. However, the actual profitability of any pairing will depend on the maximum values of the other resulting frogs. See profitable pairings for a list of frog pairings that always give a profitable result.
Selling Frogs from the Frog Mart
The Frog Mart sells frogs up to level 8 at a discount from their maximum value. You can buy and sell frogs from the market for a profit, but it takes a while to receive the frogs from the mailbox, and since the frogs only go up to level 8, you are limited to a rather small profit compared to what you can get from breeding frogs. Nevertheless, it is a way to profit.
The cash prize for first place and second place gives you a profit, but this profit is always lower than the amount that you would get if you took and sold one of the other frogs that you defeated in the race if you get first place. Therefore, if you are able to wait, or if you have stamps to spare, you can choose to take a frog if you win the race and then maximize its happiness and sell it for the best profit.
If you find decorations while hopping around on the pond, or get a decoration as a daily gift or from the frog puzzle, you can put them into a habitat and then immediately sell them. This is not a great way to make money, but you can make money this way, so I'm listing it here for completeness. Note that if you buy a decoration from the supply shop, it costs a lot more than the sell price, so it's not a way to make money.