The offering person will receive your request with a link to your profile. In response, the offer can either be accepted or rejected. If it is accepted, the swap process will be start. The current status of the swap process is accessable for both parties involved. In order to access the status, click on "ahoy, 'your name' / "my transactions" on the top right of every page.
Make sure that you have enough skillhours to transact. You can find the balance of your available skillhours by clicking on "ahoy, 'your name'.