There seems to be some confusion about "booking" a table. I wonder if it's a bit of a regional thing in English? It's incredibly common to use "book" instead of "reserve" in Australia - in fact "reserve" sounds a bit formal to me. In fact I wouldn't even consider it slang, as someone has suggested.
Around here in the U.S. Midwest, people typically say they are going to 'call for/make a reservation,' 'make reservations' or that they 'got/made a reservation' at the restaurant, normally by a phone call. It would be really unusual to say that you have 'booked' or 'reserved' a table as though you did it on your own -- I think it's something we consider the restaurant handles, plus it all may be a reflection of our car culture and planning to drive somewhere.
From what I've noticed, Brits tend to say 'book' or 'booking' and Americans (in the South) say 'reserve' or make a reservation.
P.S. I work in a restaurant. No one uses 'book' here. But as stated, I agree its completely a regional thing.
How would you say "I booked/reserved a table at the restaurant"? I rarely hear "I book a table" when compared to how often i hear "I booked a table".
Jag bokade/reserverade ett bord på restaurangen. Or, jag har bokat/reserverat … ('I have booked/reserved …')
Well, I suppose it makes sense, but you're missing some words and I don't think they quite mean the same thing.