The steps in the reloading process can be broken down into two segments: case preparation and ammunition loading. Case preparation includes cleaning, inspecting, re-sizing and de-priming cases, as well as trimming, if necessary. Ammunition loading includes priming cases, charging with powder, and seating and crimping bullets.
Cases wear over time, so clean and inspect them. Clean cases allow better inspection to see if cases are worn out, and they also reduce wear on dies. Make sure to brush off all dirt and debris -- if you have an ultrasonic cleaner or vibratory tumbler, a short ride makes cleaning quick and easy.
Check cases for bulges, cracks, splits, or other damage. If any damage is seen or suspected, discard the brass. Brass failures during firing are violent and catastrophic. A piece of questionable brass is not worth the risk of injury.
Set up your resizing/decapping die according to the instructions with your press and dies. Lubricate your brass according to the instructions as well. Run each case through a cycle on the press, which will leave it sized to factory specifications and with the spent primer removed.
Your reloading manual will have a maximum allowable length for your cases. If they're over length, they'll need to be trimmed. All of the major reloading companies make some manner of trimmer, so it becomes a matter of budget and what type of trimmer works for you. I have several styles, and they all do a satisfactory job.
Priming cases can be done either with a separate tool or on your press, if it has priming attachments (almost all do). No matter which way you go, ensure your primer is flush with or a bit below the surface of the case.
Set your powder measure per the manufacturer's instructions. Be sure to weigh each charge until you get several in a row that are consistently the amount you want. After that, randomly check that you're still getting a consistent charge. I like to weigh every tenth charge, because it's very simple to tell when I ought to weigh again.
Some folks charge a bunch of cases, then seat bullets. I prefer to seat a round immediately; it tells me at a glance what cases don't have powder, and takes out one more point where I can make an error.
Congratulations! At this point, you have loaded, functional ammo. As long as you pay attention and follow the load in your books, it is entirely safe and as good as anything factory made.
Enjoy a little economy with your shooting!