From the start you see the main window. It's the window you have your currently downloaded/downloading/to be downloaded manga.

Don't touch the tasty "Download manga" button below yet, it's evil and actually not required.
Mangafox (main functionality):
You can add manga from mangafox to the list in two ways. First is by adding manga title from a previously cached list (It's included in archive. You can re-cache it again, about it later) - basically, that's the best way to do it, - or you can do it on-line, by moving page by page, which sucks because of limited functionality, and it's actually to-be-obsolete.
- The first (good) way
The first way, click "Search" --> "Search cached manga".
You'll see a window appear with two tabs, "Search" and "Filter":

Right now, not filtered, "Search" is the whole list of manga.
Double-click any manga title and you'll get to the Manga Details window:
If you click "Add manga" on it, you will see it appear on your main window.
For your convenience, you can (and should) use Filter tab on the previous window:

You can see genre filter to the right, with tri-state boxes (Include-Exclude-Only), and obvious filters to the left. "Completed and ongoing" is a tri-state box that also allows you to filter results with only completed or only ongoing mangas. "Completed and ongoing" means both are allowed.
Textual filters have auto-complete and suggest feature.
After setting your desired options, click "Filter" button, and you'll see the results.
- The second (bad) way.
Click "Search" --> "Search manga".
Select page, press "Refresh" to load manga. Double-click manga to open manga details, click "add manga" to add it to the main window.
Now you have some manga selected for main window. It's preserved even if you exit the program.
You can double-click manga line, or you can right-click the row and select "Download manga" to get to the next window - download form.
From the very start you will, most probably, have no chapter info - it will automatically load up when you click it.
If it doesn't show up, you can try doing "Actions" --> "Advanced" --> "Re-get chapter data". If it still doesn't work, might be that mangafox downed the manga or you have some problem with internet connection.
At the top, you will see "Download folder" text box. By default, it downloads a manga named "Manga" to %Active folder%/%Manga Name%/, but you can change it, of course (See the "..." button to the right of it).
You can also change download destination of a single chapter, right-click it, select "Other" --> "Change download location". It will -not- move already downloaded manga there.
You will see a table with the following columns:
- Chapter name.
Guess it's obvious. - Chapter number.
That is, too. - Pages.
That's the amount of pages that are ready for download. Before downloading a chapter, its page info must be retrieved, so you will see it increase when it gets chapter info. - Pages downloaded.
Amount of pages downloaded already. - Current state.
No page info yet: Chapter data is yet to be downloaded.
Getting page info: Chapter data is being retrieved, you will see Pages amount increasing.
Ready to download: Chapter data is present, program is ready to download pages (or to continue downloading them).
Downloading: It's obvious.
Downloaded: Also obvious. - Download folder.
Folder that pages are downloaded to. It is set when state becomes "Downloading" - from that point on, you can right-click the chapter and select "Open containing folder".
List is refreshed automatically, but because of some nuances/me being stupid it will
stop being updated if you scroll.
To resume it refreshing, press "Resume refreshing grid" button, or "Refresh" it yourself with a button next to it.
For convenience, it is automatically sorted so that downloading chapters appear topmost. You can switch to usual sorting (by number) by clicking "Actions" --> "Sorting" --> "Sort by chapter number".
"Update chapters" checks for manga updates online.
"Get missing page info" will download page info for chapters that have it not downloaded.
"Stop all activity" stops all activity (duh.)
"Download"/"Continue downloading" starts download, 3 chapters at a time, until it's completed. "OK" closes download window and returns you to main window.
Actually, most stuff does what it says it does, I'm wasting words a lot.
Other websites:
You will need two windows here, first is "File"-"Preferences", and another one is "Download manga" button at the bottom of main window.
Here's download manga window:

First field, "Image from", marks the
first image to download. It's the one supports other viewers. You put in, for example, a URLs like following:
http://mangafox.me/manga/hitogatana/v04/c017/1.html
******************here.com/manga/noblesse/v04/c246/
http://mangastream.com/read/fairy_tail/48124549/1
Second field specifies where to download it. By default it's ~active folder/%manganame%/
Then click "Do it!" (or "Do it again!")
After that, it will continue downloading images till the end of chapter, continuing onto next chapter, and so on, until it hits the end of manga, or...
Preferences:

They're the thing that puts a stop to your download, except the end of manga. You can set amount of chapters to download, amount of traffic not to exceed, or amount of pages to download. "Reset pages counters..." switch makes the counters restart every time you start download in download window (so, it's limiting you to, for example, 10 chapters every download, not 10 chapters total from all manga you download).
These preferences
do not work on
good way of downloading (explained before).
* Cache
If you decide to update it yourself, go to Search -> Cache -> Cache manga.
Takes a while, but you'll be updated. Doing it once a month is fine, you can "Update chapters" anyway.