So, I know the sound comes out of one hole on these kinds of instruments, so direction isn't a problem. I'm mainly wondering about distance. How close should the mic be- not inside the bell, right? 
I'll really need help! Also if possible, a bit on micing woodwinds like sax and flute, too?

On that note, where WOULD I want the instrument aiming? ANd what kind of effects go on to make it shine a sparkle?

Here is a tip that most books and how to guides get wrong: Nothing comes out of the bell except distortion.  You should always mic off axis from the bell.  That means above or to the side of the instrument pointing at the body.  For a pop sound you can get close 1-2 feet.  But for a more refined, natural sound, 6+ feet is a better idea.    Ribbons are great for this, or very high spl capable condensers if recording at a distance.  Cheaper condenser mics tend to distort easily on trumpet.  It is also a good idea to cut most of the noise above 15kHz in post,  the harmonics of a trumpet rarely go past 13kHz but the noise sure does. 

For flute, place a mic about 3 feet above the players head at the side of the head joint.  You can mic from behind to minimize the breaths that flute players hate to hear in their recordings. 

Sax is easy, just point a mic at it anywhere a couple feet away.  Avoid getting too close to the bell. 

I have recorded brass on many occasions with a decent mic eg AKG 414 or U87 pointing right at the bell about 2 feet away etc. Got fantastic results. But if its the only thing being recorded then sure slightly further away and perhaps a little off axis but not too much.

Read this too it might help:

http://www.soundonsound.com/sos/mar08/articles/qa0308_5.htm

Head joint?

+ 1 on using a Ribbon mic. I've had decent results using a low budget, Chinese ribbon mic a few feet away from the horn. Add a little reverb from your DAW and you'll be good to go.

whoa, all this stuff seems pretty comprehensive of the subject! Thanks, guys. I do think it'd be tough for myself to secure a ribbon mic real soon. 
In any case, I'll be looking more into this stuff. 
Thanks again, guys!

TBH, I've never recorded a trumpet or trombone myself, but a Shure SM-58 is often a decent substitute for a ribbon in many applications. It'll handle the SPL and has similar frequency characteristics. It's just not bidirectional, so I'd think you'd want to place it a little further from the instrument to catch some room sound. Although I've not tried a 58 on brass in the studio, on stage it's the standard go-to mic for pert' near everything, including horn sections.

Read this too it might help:  http://www.soundonsound.com/sos/mar08/articles/qa0308_5.htm 

Sorry but that article seems like a load of rubbish.  Nothing above 4kHz off axis!??


For and example, and there are plenty, here is a video of a recording of Alison Balsom in a Classical context.


You can see the spot mics clearly.  Looks like a couple of AB Neumanns with a Coles 4038 pair above  and in front of the trumpet, and way off axis from the bell.  And a C414 directly to the side (which is a very popular technique).   Tell me if it sounds like it is missing highs.  

http://www.youtube.com/watch?v=ds_5cLu4FUk

Couple of points. Daniel's video is not very relevant as it is a classical situation and the trumpet is not even normal either. We are dealing with a totally different style of music. Also in that video I am sure there is also a mic directly in front of her trumpet it is closer to the music stand. The 414 on the side is not picking up the main sound I am sure of that.

Also we are talking full ensemble all playing here and as per usual with a lot of classical recordings more distant micing is being used. 

Pop trumpet is what our OP is talking about. And I am sure we are talking overdubs too. As the Sound on Sound article correctly says there are two things you have to observe.

1     They are highly directional instruments. So the players cannot afford to move about too much.

2     They are loud! Make sure the Mic/Pre/Converters, rec levels etc are set to be able to handle the SPL's involved.

I have recorded within about 3 feet directly in front with a U87 and it was very fine. Especially as Don Raider happened to be playing it at the time!