To accept the transport provider’s quote, click on "Accept Quote" in your listing (remember that you need to be logged in).
By selecting a quote, you automatically choose the transport provider and receive all contact details to your e-mail address. At the same time the selected transport provider receives your contact information and is informed about your acceptance. Contact them to finalise the transaction.
By accepting the quote you enter into an agreement with a transport provider. Any doubts concerning the transportation must be clarified before accepting the quote (see: How do I contact the transport provider?).