The image below shows how a protein is made from DNA. The CF mutation is in the DNA, this is transcribed (copied) into the RNA, splicing occurs (this means introns are removed, so exons are left), then this is translated into amino acids (three RNA bases equals one amino acid, which is why the mRNA code sequence is 4443 bases long and the protein has 1480 amino acids). The amino acids are then folded, forming a protein, which travels to the cell membrane. The protein is a channel that needs to open and allow ions to flow through.

CF mutations can affect several of these steps:
Class 1 mutations: There are several types 1) Nonsense- stop codon present. This means generally the translation stops early so the protein has less amino acids than usual and does not reach the cell surface/ or function. 2) Abnormal splicing. This means the normal mRNA and hence normal protein are not present, so it generally will not reach the cell surface/ or function. 3) Frameshift. This involves an insertion or deletion which leads to incorrect amino acids being produced after this point.
Class 2 mutations: Abnormal folding, trafficking or processing, which means there is very little CFTR at the surface.
Class 3 mutations: Reaches the cell surface but does not open properly (Gating).
Class 4 mutations: Reaches the cell surface, opens, but does not allow ions through normally (Conductance).
Class 5 mutations: Some CFTR protein reaches the cell surface and works normally, but there is less than usual (eg a splicing defect, where splicing occasionally occurs correctly, or a mild trafficking defect).
Class 6 mutations: The CFTR protein is degraded faster than usual so there is less present at the cell surface. This class may potentially also include mutations that involve the regulation of other ion channels.

Some mutations have more than one type of defect, eg a processing and a gating defect.

Sources: Google image search & Peter Mueller Presentation March 2012