So now that the law has been passed requiring a photo ID, how do you get one if you don't have/want a driver's license? Just go to the DMV and ask for a voter registration card? Will they take pictures there? What would someone need to bring with them?

Also, it sounds strange, but can I get one if I have a driver's license?

The DMV also issues ID cards that are not driver's licenses.

And that will count as a voter registration card? Or is it a separate ID for that?

Voter ID cards are separate cards.  You also can get a non driver's ID card at DMV.

http://www.fairfaxcounty.gov/elections/vregis.htm  Voter info for one county

voter registration cards do not have pictures on them.  You need a state issued ID, which you can get from the DMV for a small fee.

If you're new to the area or just unfamiliar with the voting process the State Board of Elections website will answer many of your questions about how and where to register to vote (which gets you the voter ID card), where and when to vote, and what you'll need when you go to vote - you'll find links to your locality from the SBE site.

The Virginia ID card issued by the DMV is one of the acceptable (and probably the easiest one to get, protestations of the entitlement masses notwithstanding) form of government-issued photo ID at  your polling place - and you can register to vote at the DMV (again, how dreadfully inconvenient for the so-called "underprivileged", right?)  You can go to the VA DMV ID page to see what you'll need to take with you for the state-issued photo ID.

But to reiterate the posts above the two documents are in fact TWO documents requiring two transactions.

So they do not have state Voter ID cards with a picture. If I want a picture ID and I don't have a driver's license, I have to get one of these?

For which, I need a utility bill and a birth certificate, correct?

Yes, passport will also work. May also need Proof of Social Security Number (SSN) as applicable.

http://www.dmv.state.va.us/webdoc/pdf/dmv141.pdf

If you dont drive and need a drivers license , go to DMV and get a Photo I.D. , its not a drivers license. Our DMV location also has a voter registrar's office where you can then register to vote. You will get a voter I.D. card which does not have a picture on it. When you go to vote you will need to present them both your photo ID ( or drivers license ) and your voter registration card.

You do not need a photo ID to vote in Virginia. There is a list of acceptable forms of ID on the state board of elections website.

Not currently but after July 1, 2014 you WILL need a photo ID.