You don't need to have a track-record in publishing, or be well-known, to get an agent's attention. Here’s what you have to do:
- Write a book.
- Revise and rewrite book repeatedly until it is as damn-near perfect as you can get it.
- Find an agent who represents work that is similar to yours.
- Submit your work, following the agent’s guidelines to the letter.
- Repeat as necessary.*
It's that simple. If you start with a well-written book and back it up with well-targeted, well-written queries, you'll get yourself up to the front of the queue. You might even find yourself with a couple of agents offering to represent you.
However. You’re likely to go through those steps and end up with a heap of rejections rather than the agent you were hoping for, in which case you have to consider what went wrong. Did you approach the right agents? Did you send them what they wanted? And, most importantly, is your book really good enough to be published?
If you get rejections without comments, it implies that your work is still a long way from being good enough. If you get any comments then learn from them. The more detailed they are, the closer you probably are to representation. Consider yourself complimented; then revise, rework and resubmit.
*Edited with thanks to Batgirl.