For my first novel, I'm in what's known in the industry as the "querying" stage. That is, I've finished it, edited, solicited feedback, re-edited, etc., and am now actively looking for an agent.
The process consists of researching agents who will rep the kind of thing I write, then querying them. This usually consists of either sending an email or filling out an online form, with various information they request (generally one or more of a query letter, brief author bio, a list of similar books, complete synopsis, and the first anywhere from 5-50 pages of the novel itself). Most of that I copy and paste from generic versions I've already written, though I make small tweaks and customizations constantly.
Then you sit and wait while agents go through their inboxes and eventually get to you. There's a great web site called Query Tracker that I've been using that has all sorts of statistics and information about each agent. Looking at it, I see that on average most agents request additional pages - or the complete manuscript - from about 1-2% of the people who query them. So, yeah, 8 rejections is really nothing. Once I've sent out 100, I'll start worrying. But, you know, not a lot.
In the meantime, in addition to working on my second novel (I'm about a quarter of the way through the first draft!), I've been following a bunch of agents on twitter, and seeing the writers who interact with them as well. Aside from giving a lot more insight into the industry, it is one of the most positive, encouraging communities I've seen online. Before talking to any of them, I had seen agents as sort of gatekeepers to the writing community. The first step to get past before getting to a publisher. But it's not really like that. These are people who love books and want to see more of them so actively try to find new writers to bring into the community, shepherding their works to life by adding their own skills and advice. Their twitter feeds tend to be full of advice, hints, suggestions, and encouraging words, along with the usual personal anecdotes and cat pictures, and it has completely changed my experience with Twitter.
Currently my plan is, if I haven't sold my first novel by the time I'm ready to start querying my third, then I'll try self-publishing it and start learning about marketing. :)