Without stepping on Earl's or Steven's toes, I can say that the procedure will vary depending on what is found that needs attention and where it is located.
For example, if it is a thin or pitted area in a stayed portion of the boiler (such as in the firebox area), a new piece can be rolled and then (after the bad section is cut out) welded in place flush with the existing sheet that will remain, and new staybolts installed in the new piece. A riveted patch is acceptible, but in some locations on the boiler it's not as practical as the flush patch due to variations in radiuses, etc.