What is the favorite website of a classical musician? Of course, it's IMSLP (aka International Music Score Library Project, aka Petrucci Music Library)! This is an INVALUABLE resource for all performers and students, especially the students with no money. If you're looking for a free copy of a piece...IMSLP.
Here are a few things to keep in mind as you are looking for free music.
Copyright: Yes, the music on IMSLP is in public domain in some countries, but it might not be in yours. Some music is released under the Creative Commons License; it's good to familiarize yourself with it. How do you know if the music you are looking for is in public domain? Here is the rule of thumb.
EU copyright is life+70 years. That means that the copyright holds until the 71st calendar year after the composer's death. Richard Strauss died in 1949; his music will become PD on January 1, 2020, even the music he wrote in the 1880s. Yes, this is really inconvenient for composers who had long lifespans, but I didn't write that law and am not a fan of it. Most countries in the world are life+70, so check with your country's copyright office to see if you fall under this category.
Canada is life+50 years. In my opinion this is the most reasonable copyright law. 50 years is 2 generations. Very few composers have great-grandchildren who are still collecting royalties. Life+50 means that the copyright holds until the 51st calendar year after the composer's death. Canada is unique among world countries with this law.
USA has the most complicated law in many respects. Currently, if the piece was published before January 1, 1924, it's in public domain regardless of the composer's death. If the piece was published 1924-1963 and not renewed after 28 years, it's in public domain. The US Copyright Office has catalogs it published with copyright registrations and renewals. It's well worth doing some research to see if the piece in question is in PD. I'm been surprised to find that some pieces where not renewed. These are in PD in the US and might not be in your country. If the piece was published 1924-1963 and was renewed after 28 years, it only becomes PD on the 96th calendar year after its first publication. Any piece published after 1977 is life+70 year, like EU. This is a complicated law. Luckily, for the next 40 years, each year thousands of pieces will become PD from the 1924-1963 group.
OK, enough about the copyright law.
Quality of IMSLP: The quality of IMSLP can be great and it can be sketchy. It's great because you can find a ton of first editions there. The down side to a first edition is that it might not be the latest edition of the piece that the composer produced, such as in the case of Mahler or Bruckner. Are these editions still usable? Of course, they are! If you are looking for a copy of the Franck Sonata or a Dvorak string quartet, by all means use the IMSLP copy. There is a very high chance that the editions that call themselves Urtext have copied most of the mistakes into their editions. First editions are just as good as International, Schirmer and Carl Fischer. Don't waste money on International or Schirmer if you don't have to. If there are mistakes, ask your teacher, or get a critical report (if available) on the Henle website for free and go through your first edition with a pencil. If you are looking for a list of errata for orchestral pieces, the Music Library Association has compiled extensive lists they offer to orchestras who use Kalmus and Luck's parts. Just email them and ask how to obtain a copy for your orchestral work.
The quality can get sketchy if an amateur posts his/her new typesetting of a piece. A lot of the time these don't have any more mistakes than the first edition or an Urtext edition. Sometimes these can be a huge mess, though. It's up to the performer and conductor to check these out and not just use new, free typesets as a last minute download. You can get burned by this pretty badly if you don't do a thorough review of one of these new typesets. As a professional typesetter, I can tell you that it takes a lot of effort to produce a quality product with minimal mistakes. Every edition will have mistakes, but some editions, especially the new typesets on IMSLP (and MuseScore, etc.) will have more mistakes than an average musician/conductor will want to deal with.
Not all PD music is on IMSLP: Just because the work is in PD in your country or worldwide doesn't mean that it has been uploaded to IMSLP. Maybe you should be the one getting the interlibrary loan of that piece you want to see on IMSLP, scan it and post it. There is a huge perk to members who upload and edit pages frequently: free membership and unlimited downloads without waiting.
You won't find worldwide copyrighted music there: If you're looking for Shostakovich, Walton, Britten, Corigliano, Copland, basically any composer active in the last 50-80 years, you just need to either buy the score or get it at a library. A lot of libraries and publishers will work with you if you're looking for something that's out of print, just don't expect it to be free most of the time. If it's in print, buy it on Sheet Music Plus, Hal Leonard, Johnson Strings, Shar, or even do a special order at your local music shop. A lot of small shops are willing to price match big companies like Shar.
Conclusion: IMSLP is an amazing resource. Use it to its fullest capacity. A word of advice, if you're about to send someone to IMSLP to check if a particular piece is there, check yourself first. It only takes 30 seconds in most cases.