Determine whether the suitcase is worth cleaning. If the suitcase isn't very dirty, don't bother cleaning it, or simply empty it and vacuum it off. After all, the purpose of the outside of a suitcase is to protect what's inside. Depending on the material, cleaning your suitcase could damage it. A little dust or dirt just adds character. If it was a terrible suitcase from the beginning and is now tattered and torn, or the latch or zipper is hopelessly stuck, it may simply be time for a replacement. On the other hand, if the damage is bad enough, you have nothing to lose by trying to clean it.
Empty the suitcase. Take out all the odd socks, old travel itineraries, leftover tissues. Also remove any prior luggage tags. You wouldn't want your suitcase traveling to wherever you went last month, anyway.
Remove the dust. Brush the surfaces, especially the fabric ones, with a dry brush or broom to loosen dust. Then, use the dusting or upholstery attachment on a vacuum cleaner to extract anything that is loose. Remember to vacuum inside all the little pockets on the interior and exterior of the suitcase. This is a great way to remove the small debris and trash that is left behind in the pockets. Remember to feel around first so you don't suck up any missing earrings or cuff links. Depending on how dirty your suitcase is, this may be good preparation for not making mud on subsequent steps. On the other hand, if removing the dust is enough, you're done.
Test anything wet on a small area. Take a damp cloth and, if you like, a bit of soap or mild liquid cleaner, and try rubbing gently at a small, inconspicuous area on the outside of the suitcase. If the test is successful, wipe the rest of the bag, changing cleaning cloths as necessary. Follow up with a moist cloth to remove as much soap residue as possible.
For a leather suitcase or bag only, wipe the outsides with saddle soap or oil soap formulated for leather. Use these products according to package instructions. Avoid getting leather surfaces wet.
For a hard-sided suitcase, try a mild spray cleaner. Simply spray it on and wipe it off with a cloth. Follow up with a moist cloth to remove residue from the cleaner.
Try a Mr. Clean Magic Eraser or a mild abrasive such as Bon Ami or even toothpaste to remove bad scuffs on a hard-sided suitcase. Try a small area at first, to make sure you're not making matters worse. Follow up with a damp cloth to remove any residue.
Remember that the objective is generally a surface cleaning, not a soaking.
Hand wash in a mild detergent. If you have a fully soft-sided bag, such as a duffel bag, or you are confident that water won't damage any cardboard stiffeners, try submerging your bag in cold water with a bit of mild laundry soap (such as Woolite or any laundry bar soap) or even a bit of shampoo. Swish it around in a dishpan, sink, or (if necessary) bathtub full of this solution. Then, rinse and dry the bag thoroughly.
Remember that soaking is more likely to damage the bag, leave it wrinkled, or damage or remove any built-in waterproofing than other methods, so try this step only if you think you need to.
Do not iron or tumble dry any bag that has a plastic or rubber liner. Instead, reshape it and let it air dry.
Let the suitcase dry thoroughly before putting it away.
Clean the inside. If the inside of the suitcase is lined with plastic, wipe it down with a clean, damp cloth (not the one you used on the outsides) and, if necessary, a mild cleaner. For fabric, simply vacuum it or wipe it with a dry cloth.
Spray with an odor-reducer, such as Febreze. If you prefer less fragrance, try Smells Begone.
Let it air out. Open the suitcase and all the pockets you can and let the bag air out for a few days before or after use. It will help keep your clothing from smelling just like your suitcase.
Store your suitcase properly. Chances are it lives in a closet or attic or under the bed when not in use.
Wherever you store it, cover it loosely to keep off the dust, and try to let it breathe.
If you like, put in a dryer sheet or an unused bar of soap for a bit of fragrance.
Alternatively, place some cedar balls or chips inside. Use a light fabric or mesh bag, or even a clean, old sock to contain the chips. Cedar has a mild, natural fragrance that tends to discourage insects. Look for it anywhere closet supplies are sold, or purchase a bag of cedar chips at a pet store (sold for lining animal cages).
If you would prefer your suitcase have no odor at all, try storing it with a charcoal pouch or simply a wad of black-and-white newspaper inside to help absorb moisture and odors. If you live in a very damp area, consider storing the suitcase with a desiccant pouch in it. Clean kitty litter is also good for absorbing odors and moisture.