Reinvesting the captial gains from an investment property into another property? How does that work?

It's called a §1031 exchange. It's supposed to be a non-taxable of like kind assets (i.e. rental property for rental property...etc) and the basis of your old building carries over to the new property. But be aware that this is not totally non-taxable. If you get any cash out of this deal, you get taxed on the cash received (otherwise known as boot). If any of the money due to you from the relinquishment of your property goes into your possession, it is considered boot and completely taxable. That means when you sell your property, if the real estate company is stupid enough to give you a check, you deposit it into your account for even 1 day, then use that money to buy another property. It's boot and you'll get taxed. The money can never touch your possession, it must stay in a §1031 exchange funds account. If you're planning on doing this, check to make sure the real estate agent knows how to handle a §1031 and also check with your tax advisor.

It's called a 1031 tax exchange.

I think you are talking about a tax free exchange under section 1031. This only works for trade or business property or investment real estate. You would have to find a property you want and find someone who owns the property that would exchange it with you. There are such things as three way exchanges and te are exchange networks that help with this. You end up with another property and your cost basis in the old propwerty becomes your cost basis in the new property. You would not pay tax on the gain until you sell a property or if you don't meet the rules for a tax free exchange. Contact a CPA or Attorney that deals with this type of transaction.