Well the short answer is you need a "seating die" to reset the bullet at the correct height (Over All Length) OAL. And something to measure that height (a caliper) which you can get from your local Harbor Freight.
Now having said this there are a few but's. With surplus ammo you do not know what gun powder they used when the round was made, that could be a problem, so you will need to get some "smokeless gun powder" as well. Now you need some way of measuring the amount of gun powder, this is done with a "powder scale" or dipper or powder measure. And of course you will need a set of "dies" in the correct caliber. And of course something to put the die in to reseat the bullet, a "press".
Most of the starter kits will give you most of the equipment you will need to get started, Lee make a few that I would recommend for starts, but then you will find you will want more and better equipment.
That's how it all starts, more and more equipment, then more and more parts, and more and more tools, untill before you know it you have a bench full of reloading equipment and now you have to buy more guns so you can reload more and more cases.
Just my 5 and 1/2 cents.
Jim