You can register yourself via two links: crs.uzis.cz & registrace.mzcr.cz (both available only in Czech at the moment). In order to perform the registration, choose one of the links and, subsequently, select the option called "Registrace na očkování" ("Registration to the Vaccination Timeslot Booking System"), then follow the guide through the registration and reservation process. Who will when get vaccinated can you find out in the description of the prioritization process. Well, who will then "come and serve" first?
Should you for some serious reason not be able to perform the registration yourself, you can leave it to someone else (e.g. a member of your family).
Another option is to book a timeslot via the Coronavirus Hotline 1221 (available only with Czech SIM cards), your GP also may register you. Please note, however, that he/she isn't obliged to do so, and take the quite heavy present-time load of GP practices into account as well. You should therefore use the registration via your GP solely as a last resort.
Frequently asked questions ( & answers) regarding the vaccination (in Czech only) can be found at the Ministry of Health Coronavirus Portal.