My workflow is similar to Tomas's I have my images on external drives, but I have the catalogue on my MacBook Pro. Doing it this way enables me to simply add additional drives if ( when) I need too.
However if you want to have your images on your new desktop, I'd suggest you copy them across first. That way is anything should go wrong you've still got the originals on the external drive.
Next copy the Lightroom directories across I'd suggest you locate them in the same directory as they are on the old computer.
Now start Lightroom. With a bit of luck it'll open the copy of the existing catalogue. If not it will simply assume a new install so nothing to worry about. If it doesn't select the correct catalogue simple go to File and select Open Catalog, and navigate to the correct .lrct file.
Having done that you now need to show it where the images are now living. Now if you have a root folder for your pictures, something like " My Pictures" or My Picture 2009" Click on that, the right click the mouse and select either " Find Missing Folder" Or "Update folder location" Select the new folder location and Lightroom should then update its catalog. If you don't have a root folder you will need to update each folder individually.
Run through the images to make sure all is OK. Don't delete the images off the hard drive until you are sure all is OK. Same goes for the old Lightroom files.
May sound a bit complicated but it isn't. Longest part by a long way is copying the files to you new hard drive.
