What is the most effective way to negotiate for more time while waiting for other offers?
You should consider how "in-demand" you are, both in general and for the positions in question. For the second position, if you have reason to believe that they will indeed make you an offer, you can approach them along the lines of "I would like to be able to consider your opportunity alongside my other current offers; could you give me some guidance as to when you expect to make a decision on my application?"   

For the first position, they've made you an offer, so you need to judge whether they want you there enough to give you some extra time. You'll get differing advice on this point, but I would not mention that you're waiting for another offer (unless you are confident that they will wait). Again, this depends on whether you're in a buyer's or seller's market, so to speak. No harm in asking for extra time straight out, though.

If you need more time to decide once you have both offers in hand, I think it's best to be upfront that you're choosing between offers at that point.

In general though I think you have to be much more careful about pressing the first institution unless you really think you have leverage.