Lots of good (and also divergent) responses here that should prove valuable to the OP. Let me add my views to the cacophony of perspectives.
1. I also support the position of doing the first shoot for free b/c it's a way to do some learning and building a business for you. In an ideal world, you'd start by being a second shooter for a couple of weddings. But that doesn't seem to be in the cards. If you view this as an opportunity to:
--build your portfolio.
--gain some experience (which includes learning that you may never want to shoot another wedding again for the rest of your life)
--gain a reference that may help you grow your wedding business
...than consider shooting for free. And that includes giving them a DVD of the photos with some selected edits.
Yes, that's a tremendous amount of time on your part with no formal compensation. But for someone with NO wedding experience, it's a realistic way for you to confront yourself with the reality of shooting weddings and make some post-shoot decisions about what to charge and if this is something you really want to do.
2. Recognize a risk here. You may piss off a co-worker. She may hate the work you do and tell others that's the case. You may miss critical shots. She may show your work to your co-workers (who compare it to their own wedding portfolios and think "I'm glad I didn't use her--MY photographer was so much better."). You may get in to a fight with your co-worker who expects you to edit ALL of the 300 photos that you take...or also take portraits the week before the wedding. I'm not trying to make you insecure. I'm trying to give you a reality check about shooting weddings. I know some people where they do this professionally and it's 80-95% of their business. But they go in to it with open eyes, hard emotions and cold calculation. B/c the earlier post about under-pricing yourself is absolutely true when it comes to wedding photography.
3. Other than the "i'll shoot for free", you need to treat everything as if it were the real deal. Sign a contract. Specify what you will and won't shoot/provide, when you'll be there, how long you'll stay, when they can expect to get the edits, what form they'll be in, what they can do with the photos you give them. For instance, some bridezillas or mothers of the bride will use this as opportunity to get family portraits of everyone in the family "okay, now let's get all the grandkids together, just the grandkids...okay, now let's get just Grandpa and Grandma...." and expect you to shoot 150 photos which do NOT include the bride and groom but other family members posing. I'd argue that the most challenging role for good wedding photographers isn't the photography, it's the contractural/expectation managing business. And if the arrangement you end up with is: you shoot for free or maybe a steak dinner and they don't demand anything of you and are grateful for what you give them, then you both got cheated and it's not really a learning experience for you. Treat this like a real, serious, paying gig involving $10k (except there's no money). And at the end, you won't undervalue your services in the future and you'll know if you really want to be a wedding photographer. If you view this as it's practice and isn't a real job, you'll unconsciously devote less time and effort to the edits (or won't do any edits), you won't sweat the details. And if you do the free trade with that mindset, you'll get a set of results that look like (maybe) they were shot by a well-meaning amateur who just happened to show up...and that isn't going to get you future business (except from someone who offers you $150 to shoot their wedding...but only if you include a CD of all the photos...edited!). I'm serious about this. You need to treat this like it's a real, serous, big-time paying gig with someone who is connected politically/socially and can bring you in dozes of clients at $10k a pop...except that you make no money from this gig. You need to set deadlines with the client, do a pre-wedding visit, talk to the wedding planner, think through your wardrobe and equipment, create a shot sequence list, have backup plans, have a portrait station set up on site, review other wedding portfolios to get some ideas for poses and concepts and then plan on devote a huge chunk of time to edits. A big part of your learning curve here isn't the actual photography (those that's part of it), it's the managing the client and her expectations. So treat it like it's a $10k gig.
4. They're getting a wedding portfolio for free. So you should think about asking them for some things that benefit you. That might mean letting you shoot some wedding portraits. Or posing for some shots they might not have intended to shoot (such as the bride preparing or a portrait outdoors in a scenic location). There are a range of wedding styles (like shooting as a photojournalist who is telling a story, shooting artistic photos that capture a feel for an event or location but may not look like wedding shots...like rose petals in a narrow DoF or a row of glasses pre-reception) or just the standard iconic wedding cliche poses. You may want to attempt to shoot a range of different looks so you have a more diverse portfolio.
5. And what you may very well discover from the experience of all the pre-shoot work, the client management, the negotiations with the mother-of-the-bride about what gets shot is that you hate it all. In which case this will be the best TF result you could get...a clear-eyed understanding of the hassles and logistics involved with wedding photography and a decision not to get in to it and then regret the decision later. Do NOT let them say "well, b/c you're doing this for free, we'll take whatever you decide to give us." You want to get as much value from this as you can and managing the client and expectations, working through all the details and logistics is part of it. You may decide you're a great fit for wedding photography in which case this was invaluable. But in any case don't use the fee amount (or lack of one) to justify slacking off in the prep and details.