Supplies you will need:
Minwax Polyshades in your desired color (this has the polyurethene built in) - I would buy a couple of small jars to test the stain color before you buy the big ones. Test the stain under your bar where it is inconspicuous. Sand lightly first and then apply stain. You may have to do more than one coat to achieve the desired color)
Sandpaper - Since this will be a big job, I would suggest investing in a palm sander with a fine grit sandpaper
Painters Rags (a lot)
Odorless Mineral Spirits (to clean any grease, etc off cabinet doors & frames)
1. Clean all cabinet doors and frames with odorless mineral spirits.
2. Remove all cabinet doors and set up on saw horse in the garage or back yard to stain. Do the same with all drawers.
3. Using a fine grit sandpaper, sand all surfaces to stain. Remember, you are just "roughing up" the surface so it will take stain. You are not sanding down to the bare wood. Wipe all surfaces with a clean dry cloth when done.
4. Apply stain to surfaces using a brush meant for stains. Keep in mind how many coats you will need to apply based on your test stain. Rub the stain into the surface with painters rag in between coats. This will ensure a natural look.
From what I have read on message boards, etc. this is definitely a 2 to 3 day project.
I think the darker cabinets are going to look great! You might also consider adding hardware to the doors and drawers. You could do oil rubbed bronze or brushed nickel.
Here are a few inspiration photos of what darker cabinets will look like with the current apple green wall color: