I've not been since all has reopened so take the following with a grain of salt. Lounge doesn't take reservations. I'm going on memory but I think there are maybe 4 large booths and ~12 bar stools (likely less availability now due to COVID). There's also an upper level to the lounge with some tables - maybe 6-8 (adjust for COVID). I can't remember ever having an issue with walking up but, again, that was "before" with full table/bar stool availability.
Pre-COVID they offered some good happy hour deals in the lounge but am not sure about now. It used to be that there were separate lounge and dining room menus (could order off both from the lounge) but it appears they've consolidated them for now. The menu on the swan/dolphin site seems to be different than the WDW site so I'm not sure which is accurate. If available, the crab nachos are fantastic! And the serenity cocktail is my all time favorite WDW cocktail.
The Swan and Dolphin recently transitioned to their own bus transportation (believe it is Mears) and no longer use official Disney transportation. As suggested above, could walk from Boardwalk or Yacht/Beach, Hollywood Studios or from the International Gateway/EPCOT. I think Yacht Club would be the closest- especially if you take the shortcut/path around the exterior of the Dolphin.
Hope that you enjoy it as much as we have!