Spiders are tough to kill. As mentioned above, unless you manage to spray the spider directly, the spiders will probably live through any residual insecticide.
Without calling in the pros (and in truth, even most professional pest control services don’t guarantee against spiders), about the only effective thing you can do is fogging/fumigating. Follow the directions very carefully and be thorough; you don’t want insecticide residue on any food preparation surfaces, dishes, bedding, or anything of the like. It may take more than one fogger/fumigator to treat your entire house. Prepare the house as directed (turn off fans and AC, close rooms you don’t want fumigated, cover anything you don’t want poison on, open cabinets under sinks and such that you want to fumigate, etc.), set off your fogger(s), and quickly head out. Go to the movies for a few hours or something. When you get home, open doors and windows and let the place air out for a while; most foggers recommend 30 minutes. Then, give a thorough wipe-down to anything you plan on touching or eating off of.
After that, you’ll probably find dead bugs lying around for the next few days. In my experience, a thorough fogging will keep the bugs away for two months at the maximum, usually a month, a week if you’re unlucky. But, these will be new interlopers; foggers are very thorough, and the fog should get into every nook and cranny where your non-paying tenants reside.
In general, spider control is pretty much like regular insect control. Don’t leave standing water around. Clean up food spills that may attract insects. Vacuum regularly. That sort of thing. As said above, if you drive off your other insects, the spiders won’t have anything to eat, and they’ll have to either leave or starve.