As they age, baseball cards can suffer from a variety of problems, from curling edges to discoloration, from major creases to minor nicks. The best defense against these problems is to properly store and care for cards; however, if you're buying pre-owned cards you're at the mercy of the previous owner(s) best practices. Below are some things you can do to address common problems you may encounter with damaged and worn baseball cards. It is important to bear in mind that in many cases, particularly in rare and valuable cards, repairing the card can significantly impact its value for the worse. You should only repair or clean cards that you plan on keeping in your collection, and only sell or trade such cards with clear indications as to the work that has been done. If you're interested in baseball cards as an investment, it can be very useful to visit some stores and shows, check around eBay and elswhere before you do restoration work to a baseball card -- sometimes even cards in poor condition can be worth a suprising amount of money, and your repairs will lessen that value.
The first step to the process is to carefully examine the card to determine which parts of it are damaged or aged, and which of those parts can be helped vs. which should be left alone. It is very helpful if you can compare the card to a mint or near-mint card of similar age and provenance, so that you can get an idea of how the better examples are holding up.
Frayed/fuzzy edges
It is not uncommon for baseball cards to get an edge or two that become frayed or "fuzzy" with handling. To address this issue, you will need a small metal or plastic ruler (not wood -- the edge isn't fine enough) and a modeling knife or box cutter. Place the card on a hard surface and hold the ruler against its edge. Making the smallest cut possible, use the ruler to guide the blade along the edge of the card to give the card a better-defined edge. If you have to take off a noticeable amount, you might consider repeating the process on the opposite side of the card (whether it needs it or not) in order to preserve the centered orientation of the picture.
Folded/creased cards
Typically, the best you can do for folds, creases and bends is to put the card under some weight and leave it there. Inside the pages of a book, with several heavy books on top, will generally do the trick -- or at least the best trick for which you can hope.
Marks, notes, etc.
Obtain a quality artist's eraser from a craft store. In almost all cases, you want a white eraser. Gently rub the mark with a back-and-forth motion. Try not to start and stop to check your progress -- this can lead to smudging, and even make the problem worse. Artist's erasers will generally get rid of pencil, pen, light grease, crayon and other materials. They can also help with general discolouration from dirt, but not with yellowing that can occur with age.
Ripped cards
If you have a card that is ripped, the solution is pretty simple: tape it back up. Bear in mind that while all repaired cards suffer tremendous loss of value, a ripped card is worth nothing but the sentiment.
Place the two halves of a ripped card together and ensure the design on the front and back lines up. Place a strip of clear tape over the card to hold it together.
Mold/Mildew and Baseball Cards
Baseball cards that have been exposed to high humidity or even small amounts of diret moisture can be damaged with mold and mildew. Humidity can also cause the corners to curl. To fix humidity and moisture-derived damage, put your cards in bright sunshine for a brief period -- usually no more than one hour. Set the card on cardboard or paper, not metal (which can get hot enough in the sun to do separate damage to the card) and never on the ground (which, hopefully, goes without saying.)