Plan out roughly what you want to do. Note any challenges. Get some rough idea where you intend to crop to at the end (but don't crop yet.)
'Zap the dirt'.
Zoom in to at least 100% resolution and remove dirt and scratches from the image.
Don't worry too much about things outside of your planned crop.
In images with large amounts of damage, it's often helpful to correct the smaller problems before taking on the bigger problems.
Set software tools to about the same pixel size as the damage being corrected.
Use the healing brush at 100% hardness to correct large areas of solid color, such as sky.
Use the clone stamp at 40% hardness to correct damage near sharp changes of color and/or brightness, such as a section of sky close to a rooftop. NOTE: a soft-edged clonestamp at 100% hardness works better. GIMP has several.
Faces are the most difficult thing to work on, so go in at high resolution. It may be effective to save faces for last.
Double check to be sure all dirt and scratches are removed before proceeding.
Adjust irregular brightness.
If brightness issues are minor, save this step for last; minor isses can often "go away" during other adjustments.
If one or more sections of the image are too bright or too dark due to aging and degradation, then correct them. Not all images have this problem.
Create feathered adjustment layers and alter the brightness in small increments. Change the selection areas as needed.
Preview the levels while working on brightness adjustments, in order to get a good view of which areas need work. But undo the levels previews before actually adjusting for irregular brightness.
When ready, merge the layers.
Save at this point under a unique filename.
Be sure to save a version immediately before changing the levels (except to preview). Adjusting the levels is a point of no return, so this is an important stage to save in case more work becomes necessary later on.
It's a good idea to save works in progress several times under different filenames. Use a simple notation on the filename, such as Taj Mahal1.tif, Taj Mahal2.tif, Taj Mahal3.tif, etc. TIFF or PNG should be used - they are lossless formats. Repeatedly saving as a JPEG can destroy the quality of an image, particularly if saved at anything less than maximum quality.
Adjust the levels.
This part takes some practice to get right. Remember you can always go back to the saved file.
If your software has auto settings, try both the manual and the auto settings and use whichever gives better results. Manual is usually better. Note that, especially in GIMP, adjustments to levels can cause saturation to increase; this is fine, you can fix that later.
Start by adjusting the Red, Green, and Blue levels, without touching the overall levels. In general, putting the white point at the point for each colour where the histogram says is the maximum, and adjusting the black point to either the blackest point on the histogram, or some fractional distance between the blackest point and zero (such as half-way) often works well. Exact details depend on the image. Apply the changes.
Now adjust the master levels. Or use the curves tool to adjust them with more ability to play with them.
It may, at times, be useful to do a slight crop before this point, to remove a misleading background that's throwing things off. However, be careful when doing this: You can easily crop out material you should have kept. See Step 10 for instructions. If necessary.
Adjust color balance.
This step can often be skipped if scanning yourself with a well-calibrated scanner.
This can be done manually or automatically. Manually is generally better.
Adjust saturation. The previous two steps will often have left the image a bit oversaturated.
Compare image to the original (if possible). If necessary, make further changes or restart from Step 4.
Save the image again. with a unique filename.
Rotate and crop the image.
Many digital images are slightly tilted. Generally, rotate to a tenth of a degree using the horizon or other reliable indicator to determine what the horizontal or vertical orientation should be. In most programs, it's possible to add guides to the image - straight horizontal or vertical lines that hover "above" the image. These can help. Adjust zoom as needed to judge before committing to the rotation. WARNING: Particularly with artworks, the image may not always be perfectly rectangular. Try to find a good compromise.
Time to crop. Never crop out things inherent to the image from the main file for that image. Leave in captions that were printed at the same time as the image, for example, and, when restoring something printed on paper with borders, leave the borders in: Commons' rule against borders is for ones you add, not an insistence you crop an inherent part of an artwork. Cropping too tightly severely limits reuse.
Remember: Even if you want to crop tighter for a specific use on Wikipedia, you can always upload the full image, and then link between it and a more tightly cropped version.
Final cleanup. Check the borders are good, use restoration to fix any small edge issues (for example, when restoring, say, a postcard printed to the edge, you might need to keep a little bit of damage to the edge within the crop to avoid cropping other parts of the image. You can use restoration to fix this damage. Also, you can get any dirt you left on the border now.