To remember the classification easily, use the mnemonic: "CUT the PY" $\rightarrow$ Cytosine, Uracil, and Thymine are PYrimidines. Remember that Thymine is unique to DNA, and Uracil is unique to RNA.
Step 1: Sort the bases. Nitrogen bases come in two groups. Purines have a double ring and pyrimidines have a single ring.
Step 2: Name the pyrimidines. The single ring pyrimidines are cytosine, thymine and uracil. The purines are adenine and guanine.
Step 3: Pick the pair for DNA. DNA uses cytosine and thymine as its pyrimidines. Uracil is not in DNA; it shows up in RNA instead, taking thymine's place.
Step 4: Final choice. So the pyrimidine bases in DNA are cytosine and thymine. \[ \boxed{\text{Cytosine and Thymine}} \]