I learned to reload when I was about ten years old. Granted, I mostly pulled the press handle and watched my father reload, but it didn't take me long to make my own rounds. I've had a hiatus here and there, but I've been reloading with seriousness for close to a decade after my last one. In that time period I have made lots of mistakes and learned a ton. As a matter of fact, it surprises me how much I am still learning every time I pull the press handle. It's a constant learning curve.
When I decided to get back into reloading I was fresh off active duty in the Marine Corps. I bought the Lee Anniversary kit - probably the wisest purchase to start cranking out rounds. It contains a great deal of the equipment needed to make ammunition, and I still use basically all of that equipment today. Some of the more pricey kits from RCBS or Hornady are good to go as well, but the Anniversary kit comes in right at $100.
If you are thinking about how to get into reloading, I'll give you a place to start. If you pick up a reloading kit like the one I bought from Lee, not counting ammunition components like powder, primers, brass and bullets, you will need to order dies for the caliber(s) you intend to load for, some shell holders if they do not come with the dies, and with that you can start making ammo. There are other items that are very important to have though, with the first one that comes to mind being a good set of calipers. For making the most accurate ammo, I use a comparator guage set with the calipers in order to measure seating depth more accurately, but they are not needed to start out. You will find that you can pick special items up here and there as you buy bullets and stuff.
For the most part, any of the kits that you buy will come with a reloading manual, which are indispensible for making safe ammo. If you have about $150 lying around, the best single tool that I have ever bought for reloading is Quickload. If you don't want to buy it, you can still make ammunition that is as accurate, but it will most likely take you more time. Be advised that Quickload is responsible for most of the divorce rate amongst handloaders, as husbands have been known to sit on their ass for countless hours gaming different load recipes on the computer until the wee hours of the night.
It can be overwhelming to find a place to start, so my advice is to start with the bullet for the particular cartridge you want to load for. I'll give the .308 Winchester as an example. Say you want a bullet for target shooting out to 600 yards or so, as that is the maximum distance you ever plan to shoot, but you also want to be able to shoot Bambi's baby brother if the oportunity arises. Most hunting bullets these days are not far from match grade, so pick one that will work for deer sized game -- I recommend the 165 grain Sierra Game King.
Next you need to pick your case. Usually this is limited to what you find on the shelves, but for the .308 Winchester specifically I recommend Winchester cases. As a general rule, and one I note for safety, once you develop a load for a particular cartridge, stick with the exact components and don't deviate from them; this is especially true for the case. All cases are not equal, and the capacity varies greatly by brand. If you develop a handload that is close to maximum pressure, and you switch say from a Winchester case to some Lake City cases that your bestest buddy gave you, the loads you make can damage or destroy your gun and injure you. Buy a notebook (I use the green monster books like the Marines use) and log the components of your chosen round in there with the date, seating depth, and how many you made. This will save your ass in the future. I promise that.
Now you have a bullet and case. Next you need to pick your powder. Look in your handloading manual(s) (it's best to have more than one) for the powder that gives you the velocity that you want for your chosen weight of bullet. Handloaders are living in the Promised Land of reloading nowadays; there are so many powders and components to chose from that it will blow your mind. For this post's theoretical round, I am going to recommend Hodgdon's Benchmark, as it will give you consistent velocities across the different temperatures that you will encounter in the deer stand and on the rifle range, and is known for extreme accuracy. The manual will tell you what the recommended maximum load is; start out about 10% less than the maximum charge, or whatever the manual recommends.
I find that reloading manuals from bullet manufacturers will give you the best place to start for their particular brand of bullet, and the reloading manuals from powder manufacturers to give you the best place to start for a given bullet weight. It's good to have both. You can also find reloading data online, and even order free loading manuals, like from Alliant Powder, which I highly recommend. My go-to manual is Lyman; they publish good loads that aren't too conservative and are sane.
For primers, you really can't go wrong with any of the brands out there, but I shoot CCI mostly. Magnum primers are best for magnum cartridges, but they are also useful for ball type powders and for loads that will be fired in the cold. Magnum primers often increase pressure, so know that before you start loading and work your powder charges up from there.
Here's some pro tips about buying powder and primers: ordering either one online will incur a $25 hazmat fee on top of the shipping charge. That pretty much spoils buying one pound of powder or a case of 1k primers. If you have to order, by a bunch of both to make up for the extra cost. Consolidate your order with other shooters for even more savings; online gun forums like Sniper's Hide, AR15.com, and Virginia Gun Forum have even been known to do mass buys at times, which can net even more savings from such a large order. What works for me though is to get in good with a reloading merchant who has a table at the local gunshow, and give them a call in advance with the powder you want so that they can order and bring it for you.
Yes, I have a powder dealer.
Once you find the powder that works best for your gun, buy a keg or two of it so that you have a stash that's from the same lot. You have no idea what kind of bender Ol' Valtteri Hämäläinen had last night before starting his shift at VihtaVuori plant, or how bad his multiple sclerosis has effected how much diphenylamine he can pour, so powder can change significantly from lot to lot. I had a hell of a time with Varget for awhile, and I wasn't alone.
Now that you've picked your components, head back to the manual and find out what your starting load should be. How to go about testing the right charge and seating depth for your gun is an article for another day, and is best explained by others. From my experience, it's best to find a powder/load recipe that works across the environment where you will be shooting, and the Optimal Charge Weight method has been successful for me multiple times. For those who use Quickload, take a look at the Optimal Barrel Time theory -- I've taken this information and used it to predict a handload before I even started to assemble the cartridge. It works, and will save you a bunch of time and components.
Benchmark powder is one of Hodgdon's Extreme line of powders, so it will work well throughout a broad temperature range. As you shoot loads with more and more charge, pay close attention to pressure signs (read your reloading manual for details), and your gun will tell you what it likes.
There is an abundance of reasons why you should start reloading: accuracy, economy, zombies, hoarding, for fun; these are only a handful of examples. Last weekend I seated my first batch of 9mm handloads for the purpose of hot-rodding 147 grain bullets in my Glock 17. It's hard to load economically for the 9mm, but turning it into a .357 magnum light should be fun. My kids now fight over who gets to pull the press handle, so I'm breeding a new generation of handloaders that will hopefully advance the art further than I can.