How can I find an agent after I finish writing my book?

Do an online search for book agents in your area who work with the type of material you have written and contact them. You will have to write a synopsis (summary) of your book as well as a query letter (that you address to the agent or publisher). There are specific guidelines about writing these so do make sure you learn them well in order to write appropriate ones. Some agents / publishers just want a synopsis that you send with the query letter. While others require the first three chapters of the book as well. Make sure your book is well edited and is actually ready for publication. Lots of first time writers don't realize that their book isn't as great as it seems to them. Get a second opinion (either from a professional writer / editor or someone who won't only give you praises for whatever you write).

Theoretically it is easy to answer your question but practically very hard. A practical answer to your question is that try to find an agent / publisher before you write a book.