Hi Gramps,
Well i went through this same evolution some while ago, I dabbled around in Lightroom (Blindly) didn't really get it, so stuck with PS that i'd used for ages. Then decided to make a concerted effort to use it properly.
After my pathetic attempts on my first runs at lightroom i decided to read up on it and do the job properly which was very revealing!
The workflow is quite different IMHO. Personally i think the first thing you have to do is have a firm idea of a file structure you want to use. Exactly how you want to catalog your photos and stick with it, Lightroom works with a Catalogue which is your top file structure. it creates a default structure when you install it and you can name it something more meaningful than the default. So under the catalogue name sits your file structure of folders that in library and other modes appear on the left of the screen like an explorer folder tree.
The only reason i put all this up front is, if you start using it, and don't have a clear idea of how you want to import your files into your lightroom catalogue (AKA File Structure) you can get in a hell of a mess (How do you think i found that out

). You can designate and create your file structure as you import your files.
Obviously there is a lot to Lightroom as with any other program. Things to note are....
It's non destructive as brushed on above, none of the edits are applied to your image until you export (There is NO save menu, as in save as this or that). The XMP or sidecar files holds all the layers of edits (That history list appears on the LH side in the develop module as you edit a shot). So as you edit away you'll see the history of edits increase (on the Left) but if you click right down the bottom on "Import" you will go right back to square one when you originally imported the shot to LR and you can jump around in this history to different points in your editing. The XMP file is only created when you start to edit a photo.
Exporting is managed in a few ways there is an Export manager that you can set up presets in. Here you can designate how, where, and every which way your export your files, you can even use third part plug-ins here as well. Alternatively you can use publishing services, which you can set up to publish directly to Flickr and all the other usual places. Here again you can also designate exactly how you wish to export to a service.... this will also let you update images already posted online too (Republish).
When you right click on an image after you have finished editing you will pull up a dialog box giving you export options amongst other things here, you will see an "Edit in" menu, so you will see something like Edit in Photoshop for example where it with drop the file into Photoshop for further editing (There is a set up for this in the export manager to say how you want it to export it to Photoshop ie as a Tiff etc etc).
Just another note .... on import you can set the import manager to back up the files onto an external drive or to another area in import. Mine always come into an external RAID drive on import.
Obviously there is far more to it than this but its worth reading up before you get heavily committed.
Hopefully i haven't spoken too much cobblers and it makes sense!