Buy smart. Always pick up available properties if: (1) no other player owns one of the same group; (2) the purchase would give you two or three of the same group; or (3) it blocks someone else from completing a set.
Remember that Illinois Avenue is the square most often landed on (not including Jail). The B&O Railroad also is among those most landed on; Go rounds out the top three.
Railroads are better to own than utilities, but utilities should be purchased if the opportunity arises (especially if you can get both of them). Short Line is the least useful railroad to own, because it is visited least often.
Get out of jail quickly early in the game, even if you have to pay the $50. Later on, when moving around the board is more dangerous, stay in jail as long as you can.
When you build, get to three houses as quickly as possible. The rent raises significantly between two and three houses. For example, rent on Illinois Avenue jumps from $300 to $750.
If you're stuck with low-income properties, build to four houses quickly to create a building shortage, hurting other players' chances to build. 24 of 32 houses (or 6 of 12 hotels) could be tied up on just six properties.
Avoid mortgaging properties where you own two or more of the properties. If one property in a group is mortgaged, you cannot build on any of the properties in that group.
The second set of properties on all four sides of the board is a better investment. One reason: houses and hotels cost the same to build as for the first set of properties, but the rent is higher.
The trio of orange properties is an excellent monopoly to own because of their relationship to Jail. A roll of 6 or 8 (two of the most common rolls) from Jail lands you on an orange.
Tips:
Show no mercy. If a player is down, eliminate him from the game. Luck plays too big a roll in Monopoly to risk a comeback.
Don't forget that you can buy houses, make trades, etc., on your turn or between the turns of any other players.