The manual approach would be to define a Squirrel class using the API once, then for each instance set the Squirrel instances' user pointer to the c++ class instance or a structure somehow referencing the c++ instance. Basically. Sounds easy, but absolutely isn't, as there is an awful lot of things to take care of. Almost impossible to put an example here.
From the way you put your request I relly don't recommend to take the long route, though. Try using a library like SQPlus (outdated), SQRat or the like as a start.

Though, it depends on what you want to achieve? Just to pass pointers to Squirrel which it could pass back somewhere (without any other interaction on Squirrels side) is much easier - see userdata object type.