The simplest way to achieve that is to put the play-field with the Pool Billiard coating carefully upside-down on the floor and then mount carefully the substructure on it. To prevent damage on the play-field's surface, lay out an very thin carpet or bed sheet without any wrinkles on the floor. Take care that the floor is really clean and nothing hard lies there. You could damage the surface of your Pool Billiard Table. Alternatively you can mount the play-field on to the substructure with topside-up, but then you'll have to climb around and there is a great chance that you will bang your head on the tables edge. If you do that, don't forget to switch on your video camera for funny internet-videos (I want a copy, please ;-) ). There is another reason you should do it the other way: Gravity is pulling everything down, which is really useful in this case. The positioning and everything else will be more easier if you make it the upside-down-way like discribed firstly.
Position the substructure centered on the bottom-side of the play-field like showed in the figure drawing on the left.
Use metal angle brackets.
Use at least four metal angle brackets for side frame A, at least two for each cross brace B and at least two for each table-leg.
Caution: The screws should not be longer than 20 mm. Use an arrester to pre-drill an pilot hole. Take care that the drill does not break through the play-field's surface.
Hint: Attach all metal angle brackets on the inner side of the substructure (see proposed angle bracket positions in the figure drawing).