'to ask after' someone means to ask for information about how they are and what they are doing.
· Sue was asking after you. I told her you were fine.
· He asked after my mother. He wanted to know how she was doing.
'to ask around' means to ask several people for help or information.
· I asked around to see if anyone knew someone who could rent me a room.
· When I needed to buy a new car, I asked around and someone offered me this one.
'to ask for' means to say that you want something.
· I asked for the chicken but you have brought me the beef.
· I must remember to ask for a receipt so that I can get reimbursed.
'to ask for' can also mean to do something which is likely to lead to trouble or problems.
· Walking around the streets alone at night was asking for trouble.
· If you go to that part of town, you're asking for trouble. It's very dangerous there.
'to ask for someone' means to ask to speak to them.
· He asked for Carol but there is no one working here called Carol.
· If you need anything, ask for Henry. He'll be able to help you.
'to ask someone in' means to invite them into the room or your home.
· If someone comes to the door, don’t ask them in.
· Sometimes when I'm out in the garden, the neighbours ask me in for a drink.
'to ask someone out' means to invite them to go somewhere with you.
· He asked me out so I expected him to pay for dinner.
· We often invite our friends out for a drink in the pub.
'to ask someone over' means to invite them to come visit you in your home.
· I've asked Diane from across the road over for a cup of coffee later.
· He asked me over to see what they had done in the garden.
