If you have a CCLI subscription then I suspect you can search their site for song info - I'm guessing, since I'm a novice there, but it's an obvious first call.
Even without a CCLI subscription I believe, you can use this search page:
Not every worship song is in the CCLI database... especially black gospel music... so you can also use http://www.allmusic.com. You can search by artist, CD name, etc (for all music, not just Christian). It will USUALLY tell you the composer(s) of a song. Not copyright details, but the composer at least.
To find out who the publishers are of a song, you can also search the databases at ASCAP and BMI.
CCLI is quite good but has some gaps. You also need to be careful it is actually the song you are thinking about - for example, plenty of people have written songs called 'Holy', 'Holy, Holy' or even 'Holy, Holy, Holy'. Perhaps better to start at where you got the song - for example, if it came from a CD, that should give you suitable credits. Sometimes there isn't an answer to be found without an unreasonable investment of time, in which case I don't think it would be unreasonable to credit yourself as the collector of the song, giving at least a thread to pick up in future.
There is also the question of hymns that have been reworked by modern artists. Especially if they haven't changed the melody and especially if I've ended up reworking some of the chords myself, I'll tend to credit the song to the original authors, which are probably safely under public domain. That also includes classic hymns set to established folk tunes (eg. "When I Survey the Wondrous Cross" to "The Water is Wide"), again unless something significant has been changed to make it a distinct arrangement rather than just one song to the tune of another.
Agree, that CCLI site is pretty good, can be used without a license, and can be confusing if you're looking for a song with a frequently used title. I found a youtube video a while back of a song called "Come Holy Spirit Fall On Me Now" and since the only video I found of it was from City Harvest Church, I emailed them and eventually found out who wrote it, and with that info, I was able to figure out the CCLI number for the song - which is listed in CCLI as just "Come Holy Spirit" with no lyric to help out. Sarah Reeves has a song called "Forever" that I still haven't been able to figure out and I've posted on her page, her (usual) publisher's page. Even a lot of the "official" videos on youtube don't give the publisher info.
And, of course, from time to time publishing catalogs get sold to other publishers, or fall under the management of other ones, so it's quite possible that the copyright info in a 1993 songbook is not the current info for that song.
One other thing you might do, though, would be to look at onelicense.net - they are the equivalent to CCLI but they handle a lot of the songs that are written by Catholic songwriters and some of the more "folky" authors. A lot of the music our choir does is covered by onelicense.net. Of course, if a song is covered by onelicense, then it's probably NOT covered by CCLI, so maybe we shouldn't use that song unless we have that other license. But you might also find author info on onelicense and then go back to CCLI and find the song, I think there are some songs that are covered by both.
Thank you to all of you for taking the time to reply. I am not clued up at all on copyright and CCLI subscriptions etc. as our music is covered by the diocese and it's something I've never really had to think about. You've all given me very sound advice and very useful information which I will most certainly take on board and investigate further. I guess I was naive enough to think I could just google using the correct terminology and wording and 'hey presto' I would find what I was looking for straightaway.
Again, I thank you kindly : )