If you land on a property which is unowned, and your opponent owns either one or the other two of the same colour, you will want to buy it. This means that they have no chance of getting a Monopoly in that colour. If you're getting at all short of cash, you can always mortgage it.
There are also some "Popular" properties. These are ones which the Community Chest and Chance cards often send players to. If you're not using an English board, you can always look up their positions in relation to yours as their positions are always the same. These properties are (in order of clockwise appearance, followed by ones with no exact location):
- GO (can't be bought)
- Old Kent Road
- Kings Cross Station
- Jail (can't be bought)
- Pall Mall
- Trafalgar Square
- Mayfair
- Your Nearest Station
- Your Nearest Utility
- Go Back Three Spaces
Should you have a Monopoly, congratulations! Mortgage everything you can except railways if you own at least two of them, and Utilities. Then, buy as much housing as possible. Try to leave £100 spare (in your hand) for "emergencies" if you like.
Here's another thing. If you know you have at least £100 more than your opponent (in your hand), then you'll want to auction him out of the sky. In this situation, you either want to get the property for as cheap as possible or make him pay more than the board price for a property. If you have less than £100 more than your opponent (in your hand), then you've got to make your opponent pay as much as possible. Try not to go too far with it, as then you'll end up being the one who pays a stupid amount.
If him/her getting it will result in a monopoly for them, you buy that thing regardless. You'll likely lose, especially if it's a colour between Brown and Yellow inclusive. Green and Dark Blue properties are hard to put houses on, but if they've got a lot of cash in hand you'll want to buy them too anyway. Remember that if you are buying to prevent a monopoly, you should mortgage it if it's not in the list above. If it is in the list, and you're super short of cash, then mortgage it as a last resort.