Place a dropcloth under the area where you will be working. If the paint bubbles are on the frame of the cabinet, you will have to fix the problem where the cabinet is installed. You may remove the doors, however, to make it easier to remove the bubbles.
Scrape away the bubbled paint. Use a paint scraper and gently scrape off the bubbled texture.
Sand down the surface. Use a fine grade of sandpaper to go over the area you just scraped. Extend your edges to the paint that was not scraped away to feather in your patch. This technique will make the area less noticeable when you are done.
Apply a thin coat of paint over the area with a brush. Brush in the direction of the grain of the wood with long, even strokes. Let this first coat dry for at least two to four hours, and then apply another coat. You will need to match this patched area with the rest of the paint on the cupboard. Apply as many coats as necessary. Work slowly and avoid drips.