That and Sally MacKenzie suggested I write this. Sally knows.
Congratulations! You just got the call. All of your hard work, all of the rewrites, the query rewrites and the angst have paid off. An agent (or possibly an editor) wants to work with you. This is a big deal, a big step in your professional career, so let me give some tips on how you should handle this in a way that helps make it a successful step in your career.
1. If at all possible, be prepared. Hopefully you're not reading this post after the offer came in, but instead you're reading it as a way to prepare and make a plan for when the offer does come in. I'm a planner so I like having plans. They don't have to be rock solid, but when something this important happens to me I like to have some idea of what I'm going to be doing and how I'm going to be handling it.
2. Spend some time talking to the agent making the offer. Don't expect this to happen in the first phone call, you're going to be way too freaked out, but plan to have a second phone call. In other words, thank the agent, listen to what she has to say and ask her if you can set up another time to talk when you're thinking more clearly. And yes, its absolutely acceptable to let the agent know that you're overwhelmed with excitement. In fact, I often tell authors to get off the phone, tell friends and family, and let's set up time to talk the next day when she's more prepared with questions and can absorb the answers.
3. Ask questions. This goes back to #1. There are a lot of places online where you can find lists of questions to ask an agent before signing. There is even a list on this blog (one I should probably update). In all likelihood, if you've done your research before submitting, you'll know the answers to a lot of these questions. The more important questions are those that relate directly to you and your career. Some of this will mean knowing what you want out of an agent or what you expect from an agent. Are you looking for someone who edits, who gives marketing guidance, who talks on the phone a lot or prefers email communication? Thinking about what you want in an agent will help you find the questions you need answered. Also knowing what you want from your career (hybrid, traditional, ebook, hardcover, paperback, which houses, etc) will help you formulate questions.
3. Give a time frame. Assuming you have queries and partials or fulls out with other agents you will need to give that first agent a timeframe for when you'll get back to her. I usually think 7-10 days is more than enough time. Anyone who can't respond in that timeframe isn't enthusiastic enough to want to work with you and, let's face it, you want to get your career started so waiting weeks and weeks isn't advantageous to you. So tell the first agent that you do have other agents considering your work, but will get back to her in the timeframe you've established. One little thing here. I would suggest, if you have the opportunity, to always, always, always use this time to get as many agents interested as possible. The agent offering might have been the top of your list, but that's usually not based on actually meeting and talking to the agent. Talking to other agents will give you some level of comparison to know if, yes, this agent is still the top of my list.
4. Contact all the other agents who have your work. There might be some on that list you definitely want to talk to, there might be some you queried, but already know you aren't interested in any longer (this first agent would beat them hands down). That's fine. Knowing that is great. Either way contact them all. For those agents you'd still love to work with, email (or call) to let them know you have an offer and give them a date by which you need to hear. If you've given the first agent 10 days, you might want to give these agents 7 so you have time to deal with any more offers that come in. If there are agents on that list who you just know you aren't that interested in, let them know that you received an offer and you're pulling your material from consideration. That way they won't read the submission unnecessarily and you've given up your time slot (time the agent spends reading submissions) to another author. If there are agents who you've only queried, but still desperately have on your "A" list, email them. A lot of times agents get behind in queries so giving them a chance to request and read the material only works to your advantage.
5. Wait for the offers to come in, spend some time talking to the agents and enjoy the ride. This is your time as an author, your time to make some smart decisions, enjoy the competition for your time, and find a business partner who is truly best suited for you. Go with your gut. Assuming the agent is reputable and experienced then it doesn't matter who else is with the agent or what your friends think. All that matters is that over the course of a phone call this agent feels like she's the right fit for you and your work. No one else's.
There's a kid chant, "first is the worst, second is the best, third is the one with the treasure chest." While obviously first is not likely the worst, I do think this little chant is worth keeping in mind. The first agent will often get the edge just for being first (which makes perfect sense), but in the end the agent you choose, no matter the order she offered, will be the one who is the best fit for you and your work. Her vision for your work, communication style and a general feeling of connection will be what determines who is best for you, no matter the order she came in.