Here are some useful phrases for ordering a meal in a restaurant in English:

Booking

"I booked a table for two for … (8pm).
"It's under the name of …"
"A table for two please."

What the restaurant staff say:

"Of course. Please come this way."
"We're fully booked at the moment. Could you come back a bit later?"

Asking about the menu

These are phrases you can ask the waiter if you aren't sure of something on the menu.

"What's … exactly?"
"Is this served with … (salad)?"
"Does this have any … (seafood) in it?"
"What do you recommend?"

Ordering

What the waiter says:

"Are you ready to order?"
"Can I take your order?"
"Anything to drink?"
"Would you like … (chips) with that?"

What the customer says:

"I'll have…"
"I'd like…"
"Can I have …"
"We'd like to order …"

Dealing with problems

The customer can say:

"Excuse me, but I didn't order this."
"I'm sorry, but this is cold."
"Can I change my order please?"

The waiter can say:

"I'm so sorry about that…"
"Let me take it back for you." (take it back = return it to the kitchen)
"Let me change it for you."

Getting the bill

"Can we have the bill please?"
"Could we get the bill?"
"Could we pay please?"

("bill" in British English; "check" in American English.)