Applying to a Scrapbooking Page or Altered Project:
Some chipboard letters and shapes come with adhesive already on the back. Basic Grey is one company that comes to mind. American Crafts also makes chipboard letters that are adhesive backed.
Most any wet or dry adhesive will work for altering chipboard. Where you need to be careful, is when you are adhering your chipboard shape or letters to your layouts or using chipboard on an altered item.
When altering an item and attaching chipboard shapes or letters, I recommend a strong adhesive. I use Aleene's Tacky glue. This will require you to hold it for a moment, but the hold is great. Another adhesive that will work well, is a Xyron Cheetah. (see the website that is linked below for more information.)
Adhesives for altering your chipboard letters or shapes:
When you apply paper to chipboard shapes or letters, any dry adhesive will work well. You can use your adhesive runner or tape runner effectively. I would not use glue dots because you need a complete cover of adhesive to keep the paper attached.
Check out this website for more about adhesives: