How do I find out if I have a swap partition on my hard drive?

Easy, graphical way to check with Disk Utility

1. Open Disk Utility from the Dash:

   

2. In the left column, look for the words "Hard Disk", and click on that:

   

3. In the right column, see if you can find "Swap" as shown. If so, you have swap enabled; you can click on that portion to see details. It will look something like this:

   

Alternately, open a terminal with Ctrl+Alt+T, and type swapon -s; if you see a line like the below, with statistics, swap is enabled:

In terminal, type:

free -m

If you happen to have swap, you will see how much swap memory you have left.

Use

cat /proc/swaps

In addition to the size, it will tell the type of swap (partition/file). It appears to give exactly the same output as swapon -s (posted here, but apparently deprecated).

Or

cat /etc/fstab

which will not give you the correct info in the (unusual) case of a swap added manually, as per comment by Carlo Wood.