1. Be ready to submit.
Before anything else, you need to ensure that your manuscript is ready to be read by an agent. This means that your work should be at the stage in which you would be happy with it being released to the public. You can't say that you aren't happy with certain parts and leave them to the agent and editor to fix; that's not their job.
This is where beta readers come in. They will help you see plot holes, pacing issues, spelling and grammar mistakes and the like. These all need to be corrected before an agent reads a single word.
Your manuscript is as perfect as you can imagine. Now, which agents can you query? You can't approach every agent in the world. Researching them is important. I highly suggest you search literary agencies on Google, purchase the Writers' and Artists' Yearbook or similar books, or subscribe to literary magazines to have an up to date list of agencies and agents.
When you have your list, you need to go to their individual websites. Each agency has their own policy when it comes to submissions. A few don't accept unsolicited manuscripts, others only take certain genres, and some may not have agents available to take on new clients at the time. It is vital that you read the submission guidelines as not following these usually leads to the agent dismissing your work without reading it at all.
I would suggest keeping a track of which agent at which agency you wish to query and their personal guidelines.
3. Query Letter
Some agencies will give advice on their website on how they prefer your letter to be laid out. Be careful not to deliver it in a way that is not acceptable to each agency. Does it need to be a separate attached document or part of the email? Do they want comparison titles?
Writing the query letter isn't as scary as you may initially think. It's just your way of, professionally, introducing yourself, your book, and your desire for the agent to read what you have sent them. If you are struggling, there are many examples available online.
Now, this is where literary agents rejoice in torturing writes. Not really, as the synopsis is regrettably necessary. The reason it is despised so much is, how do you manage to condense an 80,000 word story into just one or two pages?
If your lucky the agents you are querying won't have specifications on the length of the synopsis. It is unlikely however, as the vast majority (in the UK) won't accept anything longer than two pages.
I can't offer any advice on writing yours as I sent two different synopsis to an agent, and even then it wasn't right. But she still read my manuscript, so maybe there is some hope after all.
All I can say is read as many examples as possible and rewrite it, a lot!
5. Word Sample
Along with your query letter and synopsis, you have to send a sample of your work. This can come in different forms depending on the agent's specifications. Make sure you send them exactly what they have asked for. Some will request a certain number of words, whilst for most it's the first three chapters. Also check to see if they want it within the body of the email or attached as a separate document.
6. Keep A Record
There are several things you will need to add to the record of agents you researched:
Which you actually queried and when.
Their usual response time.
Their policy on enquiring after the response time has come and gone.
If you need to inform them of an offer of representation from another agent.
Whether they inform you of a rejection or not.
When they respond and what their response expresses.
7. Keep Writing
While waiting for the response, keep writing. You will strengthen your craft if you continue to develop it, and you can only do this by writing. Putting your focus into another project, or the next part of your story will ease your anxiety over the possible responses/rejections.
Please remember that a rejection does not necessarily mean your writing isn't good. It is a very subjective field and an agent turning your work down may simply mean that it isn't for them, but it could be for another agent.
Take note of any advice given and continue with your journey.
Good luck everyone.