The ATP in glycolysis is produced directly in certain reactions, the most important being the glyceraldehyde 3-phosphate dehydrogenase reaction. The process is called substrate-level phosphorylation — as opposed to oxidative phosphorylation in the mitochondrion — and is totally different from the latter.

You should read a text-book of biochemistry for the details, which are too extensive and basic to present here. Berg et al. Section 16.1 covers this well, and is available on-line.

The ATP in glycolysis is produced directly in certain reactions of the type:

X-PO₃^2– + ADP → Y + ATP

in a process is called substrate-level phosphorylation.

A key preceding reaction in the pathway is the one catalysed by glyceraldehyde 3-phosphate dehydrogenase, in which free orthophosphate is incorporated into a sugar phosphate in a reaction of the type:

Z + PO₄^3– → X-PO₃^2–

(I have used X, Y and Z because other changes occur in the structures.)

This is totally different from the oxidative phosphorylation that occurs in the mitochondrion. In both cases the (free) energy driving the generation of ATP comes from oxidation of sugars involving cofactors such as NAD⁺ to NADH. In oxidative phosphorylation the reoxidation of NADH in the membrane (ultimately by molecular oxygen) is used to set up a proton gradient, which can then be used to drive the ATP-synthase. In substrate-level phosphorylation the chemistry of the intermediates is manipulated so that particular reactions involve sufficient free energy change to drive the conversion of ADP to ATP directly. (The anaerobic reoxidation of the NADH does not produce ATP in this latter case.)

You should read a text-book of biochemistry for the details, which are too extensive to present here. Berg et al. Section 16.1 covers this well, and is available on-line.