No matter what kind of blinds you have, they can be a pain to clean. Luckily, I've found some tips that make cleaning them a little bit easier.
For Fabric Blinds: This kind of blind is generally pretty easy to maintain, and much more so than slatted or Venetian blinds. The best thing for fabric blinds is to vacuum them often. If your vacuum has varying power settings, you may want to use a lower setting so nothing gets damaged.
For Venetian Blinds: These are more difficult to clean. There are many places for dust and dirt to hide. Start with a vacuum with a soft brush attachment. This removes the loose dirt and dust. Before you use any cleaner, check the manufacturer's instructions for any warnings or suggestions about what to use. Next make a solution of equal parts vinegar and water. Get a clean sock, dip it into the water, wring it out and put the sock on your hand. Working from top to bottom, wipe off each slat. Once you have all the slats clean, flip them over and start the process again. Once you've cleaned them as much as you want, you're done!
If your slatted blinds are really dirty, more drastic measures may need to be taken. You can always fill a bathtub with water and grease-cutting dish soap and soak the blinds for about 10 minutes. Use a clean sock to wipe down each slat individually and repeat as often as necessary. Don't do this with wood or wood composite blinds, though. The soaking could warp the wood. Once you're done, hang them up to drain and wipe any excess water off with a rag or sock.