First things first: Unplug your computer before you open it up so you can clean the inside of your PC, of course.
What you need depends on what you want or want to remove from your board. Dust is easy enough: Use compressed air, a vacuum cleaner, or even an electric vacuum cleaner to blow it away. This comes with a caveat, however. You can’t use a compressed air can upside-down, because it blows air, and if you use an air compressor, they can be powerful enough to blow fragile components like capacitors if you’re not careful. If you have one and want to use it, make sure you keep it away from the board so it only has a chance to move dust. Also, do not use a vacuum cleaner, because it can create a static charge.
If nothing else, keeping the dust out will help protect the integrity of the motherboard and also reduce the risk of having static electricity that could burn the board, hopefully helping it last longer. For any residue left after using a different type of cleaner, a scrubbing brush will thoroughly clean the board.
For everything else, removing the board and using 99% (or more) isopropyl alcohol with cotton swabs is your best bet. If you want to do this, it is better to completely remove the motherboard box from the case and its components before cleaning. Although alcohol evaporates quickly, make sure you give everything enough time to dry before reheating.