Where to get started from someone who doesn't have doom for PC?

1. You can get Doom 1 and Doom 2 on steam, gog and any official place which sells Doom games. Here's alternative to official Doom iwads, called Freedoom, you could use that one. You'll also need source port to run it - something like chocolate doom, prboom+ or gzdoom.
2.There are plenty of programs people use for level design - Ultimate Doom Builder and Doom Builder X, Slade 3, Eureka. Slade 3 is also used for importing music, textures and any other important Doom level related thing. 

3. Doom has plenty of tutorials for starting if you follow them, you'll be able to cooking your first maps without any problems. Of course, you can ask questions too, most of people here are really friendly. 

6 hours ago, WhyDoIWonderWhy said:

• How difficult would you say it is to create a map from someone who hasn't made one before?

Making a map is mostly a straightforward exercise in arranging geometry, provided you follow some basic rules. The trick is to make a map that is also fun to play. This usually comes with experience, as well as observing what others have done to create fun maps.

8 hours ago, WhyDoIWonderWhy said:

• Do I need to own Doom 1 or 2 on my PC and if so, where do I get them? Or would I have to go and hunt down floppy disks?
• What's utilities do I need to make maps? Are there any available for Linux? I can use Windows-only applications but if it supports linux it's easier for me imo
• How difficult would you say it is to create a map from someone who hasn't made one before?

I'd recommend getting the games from Steam or GOG.com. As mentioned, Freedoom is a free alternative. It has a different aesthetic, though. There's also an ever-growing number of free standalone games besides Freedoom.

There are utilities available for Linux, yes. The starting points would be SLADE and Ultimate Doom Builder, though you can give Eureka a try too.

Making a map is very easy. Making a good map is where it starts getting hard; but the basics are extremely simple. Draw some rooms, then set up some line effects, adjust textures and floor/ceiling heights, don't forget to place a player start, some goodies to pick up and some enemies to fight, do some playtesting, etc. You can easily find tutorials. Here's one for SLADE. You can find plenty on Youtube if you prefer video tutorials, too.

The Doom Wiki contains a lot of information to explain technical terms and various quirks of the engine, so keep it handy.

All the info you need

Other than that, since GZDoom Builder is old by now, use Ultimate Doom Builder if you aim for GZDoom or, really, any Doom mapping format.

However, if you will simply map for original DOOM/2 use LZDoom

How did you complete them if you don't own them? Unless you played them on a console system?

3 minutes ago, Nevander said:

How did you complete them if you don't own them? Unless you played them on a console system?

I was wondering the same, but thought s/he might, perhaps, played it on a PC not owned by him/her.

On 11/15/2020 at 7:33 AM, WhyDoIWonderWhy said:

How difficult would you say it is to create a map from someone who hasn't made one before?

Easy to create a map, the editors are certainly awesome.

Hard to master though... Everyone's first map is awful, and mine's proportions had a complete disregard for movement. I recommend you start out making small maps and don't be afraid to publish your first map; feedback is a doom mapper's dream. 

EDIT: If you do decide to get into making maps for Doom, there's 4 main options for map formats.

Doom 2 format is vanilla, has restrictions on map size and it's how ID made their maps.

Boom - Doom 2 format has a little bit more features & removes some vanilla limits.

Hexen format has more features than Doom 2 format but is a weirder format and generally less used.

UDMF has the most features. You can do some crazy stuff if you use UDMF to it's fullest.

EDIT: nvm

6 hours ago, iUsuallyDie said:

Don't forget about Doom on consoles/phones as well.

I'm sure you must have read the OP and noticed that WhyDoIWonderWhy mentioned floppies and Linux. I doubt very much that consoles, okay maybe really old ones, could read floppies and neither consoles or phones use Linux. Therefore to assume the presence of a PC is not amiss.