From SecularPortal

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Membership cards are great for being able to give up when people join the society and to make it easy to check if people are members for members-only events, or for example when you have negotiated discount entry for a club or discount rates at a bar and need to prove that you are a member of the society.

They are however a fairly expensive outlay and arguably unnecessary.

Printing

The easiest way to get them printed is to do them standard business card size and have them printed as business cards. Each printer has a different "standard size" so you are best to pick your printer before making up your artwork.

If you can't print them yourself, the cheapest place to get them printed is almost always online. These aren't the best in terms of customer service and they usually charge you extra for proofs but given we're all student societies it is the cheapest way (if you don't bother with proofs, they will almost certainly come out alright, or at least close enough that those who work outside the industry won't notice, but be aware of the risks).

Make sure you licence any images you use on your artwork.