Okay, after a theological post on Psalm singing, it's time for a practical one. How can we go about singing Psalms?
Well, first you need a Psalter, of which there are many. In the UK the Scottish Psalter of 1650 is probably the best known (that's were you'll find 'The Lord's My Shepherd' and 'All People That On Earth Do Dwell'). Although it may be over 350 years old, it is a good translation of the Psalms and metrical tunes are easy enough to sing. So, if you're used to hymn singing and the King James Bible, the Scottish Psalter should be no problem. They're also easy to find and cheap, or even available for free online.
If you don't speak King James, then there are more modern alternatives. The Free Church of Scotland published a new translation in 2003 called Sing Psalms. It's supposed to be very good, as well as being in modern English. I've been waiting for ages for a copy I ordered from an internet bookshop, but if you live in Northern Ireland, I saw physical copies in the Evangelical Bookshop in Belfast last week. The Reformed Presbyterian Church of Ireland has also published a new translation recently, entitled The Psalms for Singing. Again, this is supposed to be a good translation.
A good translation is very important. Some Psalters are only paraphrases, but in that case you're not actually singing the inspired Psalms, but rather non-inspired songs based on the Psalms.
You can hear some metrical Psalms here (both from the Scottish Psalter and Sing Psalms).
As an alternative to metrical Psalms, you can hear some samples of the Psalms set to more contemporary music on the site of Sons of Korah, an Australian band who play Psalms.
Anyway, have a listen and have a go at singing.