Why are most random mutations bad?
Most of our DNA (approximately 98%) does not code for proteins at all! We're still trying to figure out exactly what all that DNA does, but since only 2% of our DNA makes protein, a random change usually will fall in the "non-coding" part of the DNA and cause no change.
Even if the mutation falls in the coding part of the DNA, it often will cause no change to the protein. This is because there is redundancy built into the genetic code. For example, if you have a 3-base sequence like AGG in the DNA, it will eventually produce the amino acid serine. If a mutation changes it to AGC, it will still code for serine! Thus, the protein is not changed at all!
However, when a mutation does a change an amino acid (or multiple amino acids), it is most likely to have a negative effect on the protein in question. Most proteins do their jobs very well so if you change a part of them, generally they do not function as well. This is why some mutations have deleterious effects on proteins and the organism as a whole.
Finally, some mutations produce beneficial changes in the organism, and if certain conditions are met, may spread in the population.
If you are interested in more information on mutations, this website is very helpful: Berkeley - Types of Mutations