Sandy,
That will depend on what type of services you are using to host you Podcast.
If you are using libsyn.
http://www.libsyn.com
You can get very good stats on the number of unique times the show is downloaded. (Does not count duplicate downloads from the same person). and they even break it down by whether the downloads were by people subscribed to your show or direct downloads from your site.
For subscribers - most podcasters use a service from Feedburner
http://www.feedburner.com
To count the number of subscribers they have. This number is based on unique hits to your RSS feed in a 24 hour basis.
Interestingly even though they calculate differently - I see very similar numbers between the two. I actually use both services.
If you are going to use Feedburner I suggest using a redirect method if you hosting company supports apache.
http://www.podcast411.com/tut_feedburner.html
Here is a tutorial explaining how to do it.
Other wise you can just get an account with Libsyn and park your MP3 files there.
Rob @ podcast411