When you query or submit manuscripts, is there a "rule" that you can only send to one at a time? For example, if you send a query to one publisher (I'm only speaking of actual publishers - not vanity publishing, and ones who do accept unsolicited manuscipts), must you wait until you hear back to send it to someone else? Or can you just send out however many copies? I would ask this about agents too, let's say you're trying to get a book published, can you send your manuscript (or part) to multiples, or just wait to hear back each time? Thanks!

Depends on the publisher and also the agent.  If you look at their website they will normally state if they require you to only send it to them.
So its best to just read what they want, follow the rules set out by that agent/publisher.  Some of different requirements to basically cut out the people who have not taken the time to do research on who they are sending too.
Also most places will list how long it normally takes to hear back from them, you can use that as a guideline, say. Agent X says he normally responds within in 2 months, you send in your manuscript, 2 months passes and nothing is heard back. You could safely send it to another agent at that time. 
You are better off seeing if an agent or publisher has certain likes and mention about that in your cover letter. If you are a fan of their genre it can sometimes help to point that out.
There is no set rules for every publisher or agent.

Some agents (and publishers) will state in their guidelines that they don't take multiple submissions. It's up to you if you want to send to that agent first and wait or send to them later down the list. For me, it would depend if it was my 'dream' agent . (most publishers will not accept unagented submissions including submissions). When asking for exclusives, publishers are usually more 'stringent' about wanting them. 

When querying, I try to send out about 5-10 at a time (or about 25% of the names of my list whichever is smaller).  The reason I do this is so that I can evalute my query through agents' eyes. One of the best pieces of advice I ever got was that if you are only querying that the agent isn't rejecting your manuscript ... they're rejecting the query because they haven't read your manuscript.

So many times writer's think there is a problem with their book when it's the letter that needs to be tweaked. I've found for me that sending about 5-8 queries gave me a good feel on how my query was working. If you send out a batch and all return with form rejection letters then take a look at your letter and see if it can be made stronger.

Hope this helps and good luck!

Most agents ask that you only send letters to them, then wait for their response. I know it is a hassle and can take much longer to get your book published, but it is better than alienating a potential agent completely when they find out you sent a query to another agency.

My best advice would be to spit shine your manuscript until you can't bear the thought of even looking at it, then edit it some more. Make your work the best it can possibly be because there are thousands, if not millions, of people just like you trying to claw their way to the top.

When you select a publisher to submit to, pay very close attention to their requirements. They will typically mention their views on multiple submissions. They will also clearly state what they want, what they don't want, et cetra. Follow these. Don't waste their time. Editors, agents, publishers -- in today's world these people will judge you by your very first sentence. If your first sentence doesn't grab them (if your first paragraph after that sentence), it's into the garbage with your work. That's a horrible thing, I know, but this is a cutthroat world we're living in.

Also, look for authors the publishing house has represented. Nowadays there should be a link to such a list on their webpage -- print that out and run to the library. Find and read as many as these authors as you can, and mention this in your query letter. Let the publisher know that you aren't another desperate fool, that you have taken the time to research them and that you will fit into their landscape.

Oh, and build up credentials. Without credentials it's nigh impossible to get published -- unless you're Stephanie Meyer and have the next supernova sitting in your lap, but even then... You need to prove that you're not just another SASE.