The simplest path will be to get a basic recording setup. Computer, audio interface, DAW software (digital audio workstation), a microphone or two and a pair of speakers and headphones to monitor the signal will be the basic starting point for most people.
The DAW software is the core of the system. That's where all the work is done. It acts as the tape recorder of old. Once recorded, you can record another track, or another 20 tracks. As many times as your heart desires. Delete tracks, rerecord them. Mix them.
There are hundreds of videos on Youtube on how to do basic recordings. A DAW that is often recommended is Reaper. It's free to try, cheap to buy, and had a huge library of video tutorials and big support community. Ardour is a free open source program. Cakewalk by Bandlab is also free. Sometimes an audio interface will come with a limited version of a DAW.
The hardware part (computer, interface, microphones) will be determined somewhat by your budget. You can go cheap, but it usually means limiting your abilities and limiting the quality. You can use a USB microphone into a computer if you want to go cheap but I don't recommend going for the cheapest USB mic on Amazon. Many are more toys that quality mics, ok for on the fly podcasting, gaming or using Facetime. If it costs $20 and comes with a table stand, it's probably not designed for music recording. Set your sights higher.
A Rode NT1 5th Gen mic has USB and XLR connections so you can do recording without the audio interface if you want, but go with a standard XLR if you get an interface and more mics. Audio Technica makes a AT2020USB version. It would get you started.