For the most part this is pretty straightforward (yay! something easy to make sense of!)
Basically, most agents (in the US, not the UK) don't need to be notified if you get other partial or full requests (unless otherwise stated!). What they want to know is if you get an offer of representation. If you get an offer (woohoo!), the industry standard is 2 weeks to make a decision (though you can often ask for a little more if you need the extra time). The next step would be contacting the other agents who have your partial/full to let them know about your deadline to see if they also want to offer representation or step aside. I'd imagine you could also notify agents still sitting on your query if they're someone you'd really like to work with. After all, there's no harm in asking! It's a big decision, so approach it thoughtfully, and make sure to be considerate of other agents' time and withdraw your queries as necessary.