What type of cell do you start with in Meiosis?

During mitosis a diploid cell (2n = two copies of each chromosome, one from each parent) replicates its DNA so that it now has four copies of each chromosome. Then it divides, each daughter cell receives two copies of each chromosome and is again 2n.

In meiosis a diploid cell (2n) replicates its DNA so that it now has four copies of each chromosome. Then it divides, each daughter cell receives two copies of each chromosome and is again 2n. Then each of these divides once more without replicating DNA so that there are now four cells each with one copy of each chromosome (1n).

You might be tempted to think of a diploid cell which has replicated its DNA as tetraploid, but this word is not normally used in this context, since this is a transient 4n state.

This is a very broad overview. Have a look at the Wikipedia entry for meiosis to get a more detailed view and extended terminology.

@mgkrebbs (in comments):

If we are considering the meiotic divisions that create gametes, then in spermatogenesis the cell which undergoes meiosis is a primary spermatocyte, and in oogenesis it is a primary oocyte. Primary spermatocytes and primary oocytes are both diploid cells which undergo DNA replication before entering meiosis I.