^Hi John. Welcome to AAAC. I have used a suede "eraser" before with limited success. If the shoes aren't soiled too badly, that might help. You can pick up one from most cobblers. Lightly brush the suede afterwards.
If the shoes are really dirty, I suggest you find a shoe shine stand you trust. I am lucky in that there's a place close to where we live that works on suede...and they do a great job.
I have had my best success using a suede eraser and suede brush. I purchased mine from J&M, but there must be many sources. Here's one that came to hand -
Some brushes have brass bristles, others nylon. Nylon can be used on any color suede, but I have found that the brass can oxidize slightly over time and mark very light colored suede.
I have stayed away from any process that would saturate the suede with solvent to clean it. My limited experience many years ago with such cleaning methods were not satisfactory, and left the shoe looking worse than before it was cleaned. Light colored suede shoes inevitably soil as worn, and I am unaware of any process that will restore them to anything resembling their original appearance.
Dirty bucks are dirty for a reason, and some soiling can add to their charm. So other than a little occasional work with the above mentioned eraser and brush, I have lived with what otherwise must occur.
Sometimes dirt just doesn't come out with a suede eraser. For those situations, I've used suede cleaners. These are not the protective sprays (that are very useful too, but that don't really clean). Here are two all-out suede cleaners I've used with pretty good results:
Woly Combi Proper. This is a spray-on foam cleaner that you then massage with a cloth or brush and then wipe off (although it will have penetrated some by then). You then let this dry completely (several hours) and then brush to restore the nap. (You don't want to be brushing wet suede.)
Storey's Suede Cleaner. This is a clear liquid that you apply with a brush or coarse cloth and rub until the suede is clean. Again, you'd let it dry completely (several hours) and then brush to restore the nap.
These have worked pretty well for me. With a new pair of suede shoes--or after a thorough cleaning of worn shoes--I give them a couple of complete sprays with WolyProtector 3 X 3. This stuff provides a protective breathable membrane that protects well against rain/water and seems to help in repelling some stains and making others easier to remove.
Note: With all of these liquid products, do a color-fastness test on an inconspicuous place before using them. I would test them on a hidden part of the tongue. You don't want significant color or lightness/darkness changes as a result of using these products. I have found with most of my lighter-colored suede shoes that the protective sprays (like the Woly one mentioned above) do tend to very slightly darken the suede.