What is the basic path to getting a literary agent? I understand that going to a writing conference helps you find one, but where can I find writing conferences? I did a search for them and could only find writing retreats. Also, is there a cost to go to a writing conference? If that doesn't work, what's a good website to use to find a literary agent that is trustworthy?
It is not necessary to go to a writer's conference to get an agent. Agent Query is an excellent resource --free, searchable, and legitimate. Other than that, your best bet is probably Writers' Market, the venerable print resource. It's available at most bookstores, as well as in an all-online form.
The basic path is just to contact agents. At one time, this used to be done by "snail" mail. A small handful of agents still prefer to be contacted this way, but most now prefer email. A few make use of online portals like QueryManager or Authors.me. Typically most agents prefer to be contacted initially with a query letter, a brief letter that introduces you and the concept of your book. They will follow up with you if they are interested. A few agents prefer the entire manuscript, sample chapters or an elaborated book proposal up front. This information will be included on the agent's website or wherever you find their listing. In general, your manuscript should be finished before contacting an agent for fiction. With non-fiction you can submit on the strength of a good proposal and a proven track record.
With that said, your presentation needs to be impeccable if you are going to be cold-contacting agents. You should read up on writing good query letters and practice the skill. And then, make sure you follow any and all specific instructions per agent --those are usually found on the agents' websites. Your manuscript (AND your letter) will also need to be 100% error free (or at least 99.9%). One last thing. NEVER pay up front fees to an agent or to find an agent, and be suspicious of any agent with a side-business. A good agent who is legitimate makes money solely from representing your book.
[Not a direct answer about conferences or websites, but it's an alternative that answers the headline question.]
Probably showing my age here, but back when books were a collection of pieces of paper there was a pretty comprehensive list of active agents in the Writer's Yearbook. These days it probably makes sense to use it as a source to find the names and then look for the agent's own website.
Looks like it's still going strong, available in many good bookshops and a few bad ones. You might find a fairly recent copy in a public library.
(This one is UK based, but it's possible that there's something similar for other locations.)
[Edit : The UK Yearbook looks like it has listings for "Overseas Agents" (ROI doesn't count as "overseas" - presumably because you can get there from the North without getting your feet wet), but a local equivalent would probably be more useful if you're not in Britain or Ireland.]