Finished compost resembles dark, crumbly topsoil and should bear no resemblance to the original materials. Compost should have a pleasant, earthy smell to it.
Using "unfinished" or immature compost that contains food scraps can attract rodents or other vermin, so make sure your compost has fully decomposed before adding to your garden beds. Conduct this simple test to tell if your compost is ready to be used.
There are a range of ways to utilize your finished compost. You can mix it into your flower and vegetable beds, blend it with potting soil to revitalize indoor plants, or spread it on your lawn as a fertilizer. Follow these links for specific guidance on how best to work with compost given the different types of plantings you are looking to ammend.