When you buy used games, they don't always have all the pieces. Sometimes you have to improvise, but it's usually not a big deal. It's easy to replace a mover or a regular die. You can find (or sell) replacement pieces on eBay. You can find whole games for good prices on Craigslist or at thrift stores.
One of the most important pieces of a game is the instructions. They tell you which pieces you need and how to use them. You can often find them online.
The pictures on the box can also be very helpful. For example, there was a board missing in a game I looked at today. It just had 7 or 8 squares on it (a start to a finish), which would be easy to replicate.
You could use beans or beads to replace the cherries in this game of Hi Ho Cherry-0 and other jewelry to replace pieces for Pretty Pretty Princess:
I was making dice the other day. You'll need to know what is on each side of a die in order to create one like it. You may be able to find a picture on the box or in the directions. I have used stickers or paper & glue to replace sides on a die. A die can also be used in place of a spinner (if it has 6 spaces).
With a game that had a few "special" cards that were missing (Hiss), I taped a small paper on a few of the regular cards to make them "special" ones, but you couldn't tell I'd changed them from the other side.
A rather difficult game adjustment I recently made was to accommodate the absence of an electronic selection device. The device tells you which pieces to pick up and move. Now we use a die to tell us which place to put things (there are 3 plates & each character can get 1 item or 2), and I made cards so players draw items that would normally be read off of the pictures in the machine.
In a pinch, you could make up completely novel ways to play with the pieces.
One of the toughest challenges is missing puzzle pieces. Apparently you can have a company MAKE a missing piece for only $13+ s/h (Jigsaw Puzzle Doctor)...