Overclocking changed a lot, its much more elegant than before, this means, its much more than just get a permanent high clock and get more fps.
In order to understand this, let me bring you up to speed.
Way back then with single core CPU's, the most obvious way to overclock is to move around some jumpers on your board, later on at BIOS level came the possibility to tinker with the multiplier. For a Pentium II 266 we would have 4x66 (aprox) and to overclock my CPU back then I changed to 5x66 (aprox) for a 333mhz OC.
Today, we have we have multi core and single core metrics, as well as GPU or CPU bound games. A "old way" overclock may not bring you the performance you want.
AMD knowing how the world changed also introduced some cool things to pump up the performance like boosting. Your Ryzen CPU has a feature called PBO.
This OC technique is different than the All Core OC and each will give have its benefits, one will give you more power towards multi core and the other to single core. Most games still won't squeeze the power of a 16 core CPU and maybe, boosting higher some cores will bring you more fps.
PUBG likes PBO
Far Cry likes ALL Core OC
Now lets end the chit chat.
You have two ways to OC, either you push all cores or adjust the PBO with curve optimizer (or even manually inside BIOS)
What is required?
Good Cooling like Noctua, Be Quiet! and so many other top brands.
Good case Airflow.
Good VRM design on your motherboard.
Finally, your questions
1. How should a Ryzen processor be overclocked? Should I use a software tool or the BIOS?
You can use either one but not both, be careful with software, because some softwares will apply settings as soon as OS starts and a bad setting will make you go to safe mode to clear the bad setting. I recommend Ryzen Master for this. As for myself, RoG boards are very good at BIOS tinkering so I go with that.
2. How much overclocking of my Ryzen processor is safe without causing damage?
Its not the OC that kills the CPU but other things such as too much voltage or pronlonged use with extreme settings causing high temperatures leading to silicon wear&tear and subsquent failure. The first warning of too much OC is a unstable and crashy system, if you can't run a full suite of stress tests then you will have to dial back settings.
3. For overclocking, what kind of cooling system do I need? Will a typical air cooler do, or do I require something more potent?
Air or Water and don't cheap out, get the BIG ONES for extra headroom. But check if the new cooler fits on your case. This is where another technique may help, undervolting.
4. Do I need to change any particular settings to overclock my Ryzen processor? The voltage and frequency need to be changed, but I'm not sure how to achieve them.
The All core OC is more difficult to attain, you need to set a new clock and new vCore higher than you would normally would to maintain stability. You will also need a beefier cooler. The curve optimizer is so much easier.
With my older 2700X I did it inside BIOS, manually overriding the PBO value and undervolting with a negative offset, so as long as there is temperature headroom for the CPU to push up the clocks, it will.
Keep in mind this is a basic introduction to the OC world, there is so much more! But I won't be very usefull, I'm just the basic to intermediate guy.
ALSO, keep in mind that all this voids warranty ; - )
