M108 was first discovered by Pierre Mechain in 1781, but it was not commonly included in Messier's catalog until the 1970's. It is now generally accepted that NGC 3556 was the M108 Messier listed. From Earth's perspective, M108 is a nearly edge-on spiral galaxy.
HOW TO FIND IT:
Find the bottom of the Big Dipper's cup. The two stars forming the cup's bottom are Alpha and Gamma. Draw an imaginary line from Beta toward Gamma. You will want to slowly scan that area until you come to a triangle of stars. This triangle will be closer to Beta than Gamma and will point inward toward the Big Dipper's cup. Look at the point of that triangle and slowly scan and stop, scan and stop, until you locate either M108 or M97. M108 should be the easier of the two and you might just barely be able to see it with a very good pair of binoculars on a very good night.
WHAT TO LOOK FOR:
For M108 look for an elongated smudge. Sometimes, it looks to me to have a saucer shape as viewed from the side. There will be a star like nucleus that should be visible. Another star on the galaxy's western side is actually one of our own Milky Way's star between us and M108.