The best way is practice -- you simply get used to anything the more you do it. When I was in HS, I joined debate club, where we spoke for 5-10 minutes at a time in front of anywhere from 5-20 club friends or opponents. When you do this repeatedly, for most people, your anxiety and nerves eventually go away, and it's just "what you do" now. The same was true of musical performance: I hated performing until I did it a…
> You can also have default responses to buy time: "Thank you, that's a great question" gives them a nice compliment and buys you 5 seconds to think. It's also important to realize that you don't need to buy time as much as you think you do. When in the spotlight, people tend to think they need to react quickly under penalty of seeming insecure. It's false. You can take a few seconds to prepare an answer and it still…
I would add that you can take a lot more time than you probably think you can, as long as you "own it" properly. If you get asked a hard question, the audience will probably realize it's a hard question. I would have no problem standing there for 30 seconds or more, saying absolutely nothing in some cases. But I would say the key is to not act anxious, nervous, or scared in that case. Just try to convey the sense that you're a sharp, qualified person, who has just been asked a Really Hard Question and needs time to ponder it.
You can do that by not fidgeting, and by controlled mannerisms: look up and out into space, but in an obviously conscious manner... or chew your bottom lip a little and furrow your brow... or steeple your hands and look at your hands while also having a furrowed brow, etc. There are other ways to communicate what I'm getting at, so just experiment. What you don't want is a "deer in the headlights" look, or that stereotypical "blank expression" that conveys "I have no clue what's going on right now."
The key point is, you don't have to have an immediate answer to every question. Pauses and silence are OK, to a point.