When someone makes a request for a connection to you, you will receive notification of a connection in two different places the next time tht you login to your account, in private messages and under your connections button in your profile.

The first thing to do is to go to the connections button and accept or deny the request. There is a green check mark and a red "X". By clicking on the green check mark, you accept the connect onad by licking on the red "x" you do not accept the connection request. It's that simple. You can then send a private message reply to let the person know that you have accepted (they will be notified in their profile also) and whatever you would like to keep in touch with that person about through the new connection. You do not have to send a response, however, if you do not want to.