It could affect a protein a few different ways:
1. If you get a switch of one nucleotide for another, this could (but not always) result in a different amino acid being inserted than was supposed to. So, for example, you were supposed to insert a methionine at AUG of the mRNA, but the mutation resulted in GUG which now codes for valine. This may disrupt the activity in the protein - either in proper folding or if in the active site of an enzyme could disrupt the activity.
2. Other swaps of nucleotides can result in shortened proteins - so if you were supposed to have tyrosine inserted at UAU and that got switched to UAA which is a stop codon, then the protein is too short - and may not fold or function correctly. Depends where the mutation is of course.
3. Of course take that further and perhaps you were supposed to have a stop codon (UAA) and that got switched to UAU...so now instead of stopping the protein synthesis you instead insert a tyrosine and the protein continues to be extended until another stop codon is reached...that could be disastrous for the function of the protein as it probably won't fold properly.