Hi Amazilla and welcome to the forums.
You have found the right place for informative and helpful people. The Members on this forum seem to know almost anything to do with turning and are more than willing to share that knowledge.
Are the chucks you have bought like the ones you see in power drills? If they are then they are not intended to be used in the headstock of the lathe. They are for use in the tail stock to hold drills when boring holes etc.
The best thing to do is let these good people know which model lathe it is and they will advise you what accessories you need to get that will fit.
If it is a Fox F46 251 Midi Lathe - 10"
Technical Specifications:
Motor ... ¾hp Induction
Speed (variable) ... 410rpm, 650rpm, 1030rpm, 1500rpm, 2200rpm & 3050rpm
Distance between centres ... 15" (375mm)
Swing over bed ... 10"
Thread ... 1" x 8tpi
Tapers ... Morse No.2
Tail stock spindle travel ... 2¼" (60mm)
Weight ... 35Kg
The main measurement is the spindle thread 1" x8tpi. Can be found on the outside of the place where you were trying to fit the drill chucks. This is where you will screw mounting attachments like face plates, chucks etc.
If you are totally new to turning I would advise looking for a local Wood Turning club and going along to a couple of meetings. Also do some research online. There are literally thousands of Videos on Youtube etc demonstrating basic and more advanced techniques.
I only took up the hobby about 3 months ago but the advice above was some of the best I have ever received.
Look forward to seeing your creations in the future.