If you do the booking on the Deutsche Bahn website, you should not be able to book a train with compulsory reservation without reservation. In these cases reservation usually is included in the regular fare and doesn't cost an extra 4.5€ as with other tickets.
You can check on your ticket. If a wagon and seat are mentioned, you have your reservation. There should be a note like "ICE 123, 1 Sitzplatz, Wg. 22,
Pl. 24, 1 Gang, Tisch, Nichtraucher, Handy, Res.Nr. 8123 4567 8901 34" including the reservation number, wagon (22) and place (24).
If you booked a full price ticket and want to use another train, you have to change the reservation.
In general, you can get a reservation on most trains by going through the normal booking process and select "reservation only" when asked during the process. (There are trains that can not be reserved (regional trains mostly) and some that can not be reserved online (some international connections))