Most of what you do is in Mugen.cfg, Select.def, Fight.def, and (insertstagename).def, and most of these you can find in the Data folder once extracted.
Step 1: Download Mugen (ideally hi-rez, if not, make sure any stages or screenpacks you download are low-rez or don't say hi-rez).
Step 2: Download a Screenpack.
Before you do anything make a backup of the Data folder as if you mess up, you can always reset it to what it originally was. Most screenpacks, lowres or hirez simply ask you to dump a few files into the data folder and replace the old ones, simple, no? Just make sure you're using a hi-res Screenpack for hi-res Mugen and not a low-res one or vice-versa.
Step 3: Download a Stage (remember Hi-rez stages for Hi-rez mugen, they don't work for anything else, and low-rez stages for low-rez Mugen).
Put the .sff and .def files of each stage in here, and then open up the .def file with Notepad and specify what music you want (make sure the file name is accurate to the music file you want to use, I use custom). Then just make sure you put the mp3 of that music in the Sound Folder. Lastly, go into the Data folder, and open up Select.def and scroll down and put the name of the stage in the "extra stages" area, the text file explains it all.
Step 4: Download a Character (this takes time, I suggest going here: http://mugencharacters.ucoz.com/).
Once you've got a character, put his/her folder in the "char" or character folder. Open up his folder and take a look at his files..MAKE SURE all the files have the same character name, case-sensitive AS THE FOLDER, that is to say, if you have a Sol-Badguy folder, make sure every file in there is called Sol-Badguy.air, Sol-Badguy.cmd, Sol-Badguy.sff, and most important of all Sol-Badguy.def. If it's not the same name as the folder, either change it, or make sure you specify the .def file name in the Select.def text file. i.e. something like "VENOM/EddieBrock.def". You can find Select.def in the Data folder with everything else. Because I like tweaking my character select, I keep a shortcut of Select.def in my character and stage folders just in case I need to tweak something, make sure you save the name of the character/folder/path in the select.def.
Other things:
I like to keep my folders CLEAN so they aren't cluttered with patches or backup folders, so keep those elsewhere. You can gather up to several Gigs of data from this alone so make sure you have the room.
Some characters are HARD AS FUCK OR BROKEN, so what I like to do is make a tier-list of the characters in the select.def file, you know where it tells you the "order=#"? That specifies how often you're going to fight that character in arcade mode. Scroll further down and you can specify how many fights you want in Arcade and how frequent they are, it explains it all...so for broken characters here's what I do in Select.def:
Notice the semicolons?...I basically commented out a character, or as I like to call it...BANNED them.
Hope that helps.
Lastly, some tips regarding Mugen.cfg (found in the Data Folder)
Set it to 640 x 480 (or more if you have a big monitor), make sure the setting for DoubleRes is set to 4. Make sure it says Windowed, Turn off Debug, Turn on Window Stretching, you'll have a lot less headaches if you do. Ctrl+Enter for Full screen if you want it. The text file explains the settings in detail. Make sure color settings match those of your system hardware.
Once you start mugen, go into options and tweak everything right away, I set it to easiest setting and normal speed, turn off timer to cut back on hassles. Then just set up your inputs, then save your configuration. Exit out, give it a try.
Mugen is all about testing and trying stuff out to see if it works, and if it does, have fun. If you don't know how to use a character, go into their folder and check for a Readme/Leeme file, it may have a movelist for you.
Lastly, KEEP A FRESH DEFAULT BACKUP of all your files (or just keep them zipped) in case you mess up! I can't tell you how many times I've had to restore files because something went wrong.