A lot of different programs, files, and websites are super handy when working with chiptune. I’ve compiled the ones I use most often here to help support anyone’s journey.
The music programs I use (all free):
Furnace Tracker: The premium free tracker for nearly any system of your choosing. While the interface is not the most approachable, its utility for FM chips cannot be understated.

Deflemask (free legacy version): A more bare version of the paid tracker program, Deflemask. Moderately easier to approach, but has bugs that will not be fixed as it no longer receives support. If possible, stick to Furnace.

Audacity: A feature-rich audio editor used by millions. Very helpful for analyzing dense audio using features like EQ to isolate frequency ranges and Change Tempo to slow down portions of songs.

OpenMPT: Sample-based tracker compatible with a wide range of file formats. I have not used OpenMPT for composing myself, but it is popular for those preferring sampled music like released on DOS and SNES.

VGMusic Studio: Music player and visualizer for GBA and Nintendo DS music. I don’t compose using it, but have found it helpful to separate music released for those systems by channel.

BambooTracker: A tracker focused on the YM2608 OPNA chip. Jake Kaufman composed the excellent Shovel Knight Dig OST using BambooTracker, and has made his modules available from the album Bandcamp page; alternatively, you can download it by clicking here.

Tools for ripping and creating instruments:
VGMRips.net: Website with audio content from thousands of games. The .vgm format contains the commands sent to the chips rather than the output sounds themselves, which allows for extraction of many useful properties from the composition side (how the instruments were programmed, sequence data, etc). Search the site by game, composer, sound chip, game system, publishing company, and more! Besides being a handy resource for composers, with a free account you can also create/listen to your own playlists and share in forums with others.

Vgm2pre: Tool for ripping YM2612 instruments from .vgm files (which you can easily get from VGMRips.net above). Interface is pretty bare but appropriate for the single-function program that it is.

Dexed: A synth program imitating the Yamaha DX7 keyboard. A handy virtual tool to use alongside the pdf below.
FM Theory and Applications: Guidebook on FM for music written by its inventor, John Chowning. This level of understanding is definitely NOT required to start making songs, but can provide valuable depth to inform instrument design when one feels ready.