Well basically, you want to start out at the beginning with the number you're being asked to convert. For instance, here's a problem:

Convert 345 centimeters to miles with the conversion factors 100 cm = 1 m, 1 m = 3.28 ft, 5280 ft = 1 mi

The problem is asking you to convert 345 centimeters, so that's what you start out with. Then, you should look for a conversion factor (it may not be given for you, like I did here, but there will be a conversion factor out there for your problem, I promise! :]) that includes a value with the same unit. Since 345 is in CENTIMETERS, or cm, the next conversion factor/proportion you would use is 100 cm = 1 m. Now your conversion looks like this

345 cm x (1 m/100 cm)

The reason you multiply by one thing divided by another is because 1m/100 cm is equal to one, since 1 m and 100 cm are, as stated above, equal and the same thing. The thing with dimensional analysis is that you want to convert units, not change the original value. That is why every time you use a conversion factor, it must divide out to become 1. The 100 cm is on the bottom is because you can only cancel out units if one is on top and one is on bottom. Now, after you cancel out the cm, you are left with the unit METERS, or m, on top. Now, you repeat the process - look for a proportion given that has meters as the unit. In this case, you would be using 1 m = 3.28 ft. Now your equation would look like this:

345 cm x (1 m/100 cm) x (3.28 ft/1 m)

Continuing on...your overall equation should look something like this: