The short answer is, "a lot".   Exactly how much you will save depends on the caliber(s) you will reload.   The table below shows the typical savings that you can realize on some common (and not-so-common) handgun calibers by buying good quality jacketed bullets and other components in bulk, using your own brass, and loading them yourself.

The retail prices per 50 cartridges, and are from a famous big-box outdoor store in December of 2018.   The costs for bullets and primers came from online bulk retailers on the same day (prices include typical shipping and hazmat fees).   The resulting reloads will be as good as or better than good factory ammo.   (For the records, it's not an apples-to-apples comparison, because the retail prices for the ammo are per box, and the component prices are for bulk quantities, but bear with me here, I'm trying to make a point).  

Notice that you'll save the least when reloading ‘commodity' calibers such as 9mm, 40 S&W, and .45 ACP.   With these calibers, most of your cost savings will be due to the fact that you'll be reusing your brass.   Even so, if you shoot a couple of boxes of 9mm per week, you'll more than pay for a basic progressive setup in the first year.

The retail price for less common handgun calibers is much higher because the manufacturers make it in smaller lots, and the demand is lower.   This is where reloading really pays off.

The savings is greater still when reloading rifle cartridges.   A couple of years ago, a friend bragged about the great deal he got on a barely used Weatherby rifle in .340 Weatherby Magnum which he planned to use for elk hunting.   The bragging stopped when he found out that the ammo he wanted to use was going to cost $6 per round, and had to be special-ordered.

Fortunately for him, his rifle came with a few boxes of once-fired brass.   After a $375 investment in equipment, he was able to buy components and reload ammo identical to factory for $1.50 per round.   His complete setup was ‘paid for' before he fired his 84th round.

The savings becomes downright astronomical if you cast your own bullets.   For example, you can cast and reload very high quality gas-checked 500gr S&W .500 flat-points for about $0.20 each, which represents a savings of over $2500/1000 rounds when compared to factory ammo.