The worst part is that most of the time, this is easily avoidable with just a little extra effort. Here and now, I'm gonna show you how to correct this.
(Remember that even if you don't care about us poor American scrubs with our slow, monopolized internet connections, a lower filesize will definitely make your mod more appealing for people to download if it isn't shit.)
IMAGES
Now, say we've just got this sweet texture we want to use for whatever reason. In this case, it's two planet-sized robots ready to duke it out to the death in the clouds:

Now this'll look great as a part of my new 27-layer skybox in my latest UDMF masterpiece! Except...

1.11 Megabytes. Even for an image of this size that's way too much. This will hurt not only download speeds, but also performance. As it will take up a lot more than 1 MB of ram while in action, this will only get worse and worse as you add in the other 57 skyboxes, Curly Brace, DecorACS monster abominations, and 32 hours of WAV music you've got planned.
But this can be rectified by getting to know a few gems of a program your lord and masters for the moment:

Pngquant, a badass PNG compression tool; Paint.NET, a GIMP/Photoshop clone with an interface that's actually usable by humans; and Audacity, a radical sound editor. Praise them. Or they'll f*ck you up.
Now it's very simple to just try and lower the resolution of the image. That's a great idea, but say you don't want to do that for whatever reason. If it's not anything with transparency you'll probably want to use JPEGs:

The lovely thing about JPEGs is that they allow for great compression at a negligible loss of quality for things like photographs, desktop backgrounds, and stupidly high-res textures. It's better to tweak the quality just right for your image in particular. And remember: they also tend to work best with large images, as that's when the artifacting is the least noticeable.
But say you're wanting to compress a sprite, or any other image that requires transparency? Say that for some reason you want the maximum quality versus size in a palleted image? Well, pngquant may just be your savior:

A curious beast, pngquant will devour images and spit out heavily optimized versions. One cool thing about pngquant, though, is that it supports alpha channels. Just drag and drop into either the 256 color or automatic color batch (I use automatic because I'm lazy) and...

Huh... Well... It's done something weird here. Looks like it made two pictures, but what's the difference? Well, the fs8 version weighs in at 628 KB and is dithered extensively, while the or8 version weighs in at a whole whopping 330 Kb and is slightly posturized. But which one to chose? Well, at a glance they all kind of look very similar:

(Which one is which? lol)
So I guess just choose the smallest one. This gets even more indifferent at lower resolutions, there you'll just have to pick the best-looking one, and I guess it's the same here, too. Seriously though, it's probably best if you chose sane texture sizes instead, like consistently things that are Doom-sized, just use Paint.NET's resize tool for that.
AUDIO
But what about your hours of audio? Your band's excellent new album must not go without excellent distribution, how do you make sure all the sad little Americans and Australians with their horrible monopolized internet get your mod that you worked so hard on? I mean, take a look at this!

Good lord, how will we ever fix this mess? Oh wait, I guess this is where we use Audacity.
The nice thing about Audacity is that it allows you to do general sound editing, so with it you can make sound effects that are unique to your mod, or you can lower or increase the volume of a song as needed. But in this case, all we need to do is compress our song.

Here we can do things like set the project rate to 44100 HZ (only X Men will notice a quality increase above this) and export it.

Don't save it is MP3 because that is what filthy neanderthals do. Save it as OGG instead.

It's best to export at a quality level of 5 or lower (0 or 1 for SFX) because it allows for a far higher quality than MP3 at a significantly lower filesize. Another reason to use OGG is that it also decompresses much faster ingame. And in this instance our final filesize is is only 3.1 MB even at the highest sane quality level. Technically we could reach sizes of 700 KB just by sacrificing (quite) a bit of audio fidelity.

Well, a silly man would tell you to do all this manually, but once again good ol' Audacity has a few neat tricks that'll make your day much easier.
There's this thing called chains and a tutorial for it on the Audacity Wiki. But that is complicated and I am a simpleton. So I just load multiple files into the window, do whatever to them, and hit "export multiple". This gives me better control of the project rate and what effects I want to apply and does about the same thing in the end. Here's a picture of Audacity exporting:

Hey look.
But say you don't have your own band to make songs you can use, say you have no musical talent whatsoever and don't want to use royalty-free music, or music from other artists that could run into copyright problems?
There's the 'technically not legal but still tolerated by the corporations and the /idgames archive' art of taking music from other video games. Well, if you're using anything from a game that uses any form of synthesis (whether it be FM, chiptune, or sample sequencing) it's definitely better to use rips of the songs; there's a reason most early games were as tiny as they are so make the most of it.
These rips can be found in many places, but the big thing is that they are emulated by Zdoom and so can be handled like any other music file. This is most convenient.
TEXTURES
So now that you are compressing, I bet that you've come to a confusing thing, say you want to cheaply combine two textures, just layer one on top of the other. So you've already got both textures in your mod, what now, do you just combine them with Paint.NET?

No! Zdoom and all it's babby ports (Yes, even Zandronum surprisingly!) have something that does generally the same thing, it's called TEXTURES.
Now a TEXTURES lump is a bit of a bitch to make, just make a new entry and name it "TEXTURES.TXT". Now select the entry, click on the "View as Text", then open the "Text Language" dropdown menu and select ZDoom Textures. Now just put two forward slashes (//) without the commas, and then save the entry. If you did it right, it should look like this:

If it doesn't look like this, you did it wrong so go back and do it right.
Open up the thing. Now I could go into extreme detail about how to do a TEXTURES, but there's probably 37,000 different tutorials out there, and It really is quite simple. Just make a new texture, and add the patches from your mod file like this:

You might as well call me Vincent Van Gogh because I'm craaaaaazy talented.
CONCLUSION
Well, I hope this guide serves to help someone somewhere, and that I didn't accidentally do something illegal in the process of making it. Remember everyone: I only had the best intentions! If you have any suggestions of things to add or touch up, just scream at me below. Although, I guess I could leave you all with a tip:
We are living in the year 2015, so please, please, please, do yourself a favor and use PK3 files built with 'store' or 0% compression. It's much neater, lowers loading times, and is probably a better choice for large projects. Just look at Ao Oni Doom, under the hood that thing's a goddamn mess of a WAD file and is an example of exactly what you shouldn't do (Did I mention that it's also 96 MB?).
And here are some important links to check out for all the things I found:
http://www.getpaint.net/
http://pngquant.org/
http://audacity.sourceforge.net/
http://manual.audacityteam.org/o/man/ch ... ation.html
http://project2612.org/
http://snesmusic.org/v2/
http://www.zophar.net/music.html