Acquiring sheet music
If you're going to rehearse and perform music, you need a full score for your conductor and a set of parts to distribute to your musicians. (For any non-musicians reading this, the score has all the music written in it so the conductor can see everything that's supposed to be happening all at the same time, and the parts just show what the individual reading it is supposed to be playing, like, say, an oboe part.)
For the purposes of music acquisition, there are really two categories of music you need to worry about: music in the public domain, and music under copyright. Public domain music is usually easily available for free with no constraints on performance. Copyrighted music is more difficult (and costly!) to acquire.
In the US, any music published after 1923 is still under copyright (unless the composer has specifically not copyrighted it or has made it available using a Creative Commons license or something else similar). Because of some complicated treaties I don't fully understand, no works written after 1923 will enter the public domain until 2019. See this website if you want to read about this subject in excruciating detail.
So, basically, the old classical warhorses like Beethoven and Mozart are in the public domain, and contemporary pieces are still under copyright. However, even some "classical" composers like Prokofiev were recent enough that their works are still under copyright.
Public domain music
The complete scores and parts for many pieces of orchestral music in the public domain are freely available for download from IMSLP, the Petrucci Music Library. All the Beethoven symphonies are there, for example. If you pay a very small annual subscription fee to the site, you can download stuff without the otherwise-imposed delay time, which might be worth it if you're going to be downloading a lot of music.
Music under copyright
To acquire copyrighted music, you need to borrow it, purchase it, or rent it. Complete scores and parts are not cheap, so if you're going to program copyrighted music, be sure to do your research in advance and include the rental fees in your budget.
Additionally, if you're going to perform copyrighted music, you are responsible for purchasing performance licensing. The right to perform the music in public is not conveyed by simply renting or buying the sheet music.
Some copyrighted (and also non-copyrighted music) can be borrowed from libraries. The Fleisher Orchestral Music Collection at the Free Library of Philadelphia is a fantastic resource, and they will ship the music anywhere (in the US at least, not sure about abroad) for just a nominal fee.
Some other large public libraries also loan out performance sets, but only to organizations within the geographic areas they serve. For example, the Los Angeles Public Library, the New York Public Library, the DC Public Library, and the San Francisco Public Library have such collections.
You could also check with local university libraries. However, if the university's orchestral music collection is owned by the music department and not part of its circulating library collection, you might not be able to borrow it. You are not supposed to borrow copyrighted music from another orchestra because this constitutes copyright infringement.
If you're going to borrow music from a library, reserve it well in advance (in case someone else decides to check out the same piece as you). Also, either go check it in person in ahead of time, or ask a librarian to go make sure it's actually on the shelf and has all the parts. The RCO had a nightmare with a Shostakovich symphony which was in the library catalog but wasn't on the shelf, and, as far as anybody could tell, had never been on the shelf.
Some complete sets of scores and parts are available for purchase from the publisher. It's unclear to me why some music is available for purchase and some isn't. If you're going to buy some music, make sure it's actually the score and parts and not just the conductor's score.
Many, many pieces of music still under copyright are NOT available for purchase at all, and if they've never been available for purchase, you probably won't find them in a library either. (You might be able to buy the score but not the parts.) The parts are available to performers only through rentals from the publisher. You sign an agreement with the publisher and pay the rental fee, and they physically mail you a large box with all the parts in it. You rehearse and perform the piece, and then you mail all the music back to them. It's sort of like borrowing something from a library, only weirder and a lot more expensive.
And sometimes truly weird stuff happens! For example, the Dexter Community Orchestra rented a piece, and after a week or two, the publisher contacted us to say that the Chicago Symphony Orchestra wanted to rent it also. The physical set of parts the publisher had shipped us had the Chicago Symphony's markings and bowings written in (they'd rented this set of parts before), and they wanted us to exchange the parts we'd been given for a different set of parts so that Chicago could have the set with its markings. So we boxed the music back up, and the publisher sent us a different set.
This all seems horribly archaic and logistically stupid to me, in this digital age, but regardless of my opinion, this is the way the industry works, and there seems to be no avoiding it. If you're going to rent music, plan waaaaay in advance, and do your homework.
The rental fees vary quite a bit, but it's generally not cheap. The RCO rented a Rodrigo concerto, and it was about $750 for this 20-minute piece we performed once. Additionally, amateur orchestras typically need a longer loan period than professional orchestras because they need more time to rehearse, and you might have to pay an additional fee for that longer loan period. (This is a regressive fee structure that I personally think discourages amateur orchestras from performing newer works and thereby actually causes more harm than good to the composers that these fees are supposed to support, but I'll get off my soap box now...)
When you rent or borrow music, you're not technically supposed to photocopy it. However, I highly highly highly recommend against distributing the original parts to your musicians because inevitably someone will lose a part or their dog will eat it or something, and you'll have to pay a stiff replacement fee. I recommend you photocopy the parts anyway, and then collect and destroy the copies when you're done.
If you do photocopy it, you still have to have the rented parts in your possession during the time period you're rehearsing and performing the piece. You can't rent it for a day, photocopy it, send it back, and then perform it a month later.
Also, when you get the music, even if you decide not to hand out the originals to your musicians, make sure you make a checklist detailing exactly what parts were sent to you. The parts will probably be numbered so they're easy to track. This way you can be absolutely sure you've kept track of all the parts and returned everything, and you'll know if anything is missing. If you do hand out originals to your musicians, make sure you write down exactly who took which part so you know who to nag if you don't get a part back.