You are under no obligation to tell a new agent/pub requesting the full that your full is out elsewhere. Unless they ask, and then you have to decide whether you want to share that info. or not.
If your manuscript is not under an "exclusive read" clause from an agent or pub. (and, to be honest, I don't recommend doing that) then you simply send the full as requested.
Now, when someone makes an offer, you must immediately inform any other agent and/or pub. that you have received an offer -- usually this is a good thing, because it means they will either a.) read your book immediately if they are truly interested, or b.) pass on your book, which means they were never that interested in the first place. You then can give the ones who are still interested time to read your manuscript by telling the offering agent/pub. that others are reading your full and you need to let them (the offering agent/pub) know your answer in a week or two. This is standard practice, and no decent agent or pub. will get ticked off over this.
So, when the first offer happens, tell the offering agent/pub. "I'm thrilled, thanks (etc.) but I need a little time to consider. I'll give you my answer on XYZ date." Then tell the other agents/pubs you need THEIR answer (whether they are still interested or not, their counter-offer, etc.) a day or two BEFORE the date you gave the offering agent/pub. This gives you time to get info. from everyone and consider your next action.