When I download a DVD torrent, it's made of multiple files such as VOB, BUP, IFO, etc.
How do I join all these files into a single DVD file?

There is no need to join anything. Those files are exactly the files like they are stored on a DVD in the folder called VIDEO_TS. If you burn them in a folder called VIDEO_TS as data to a DVD-R, the disk should play like a DVD on your computer or a stand alone DVD player, means with menu navigation, chapter and language selection etc …

Video player on computer will usually play those DVD Data files like a DVD, if you select the VIDEO_TS.IFO file to play (that is the DVD main index file).

Of course it is possible to create a DVD ISO image from these files, e.g. with ImgBURN, but that has no advantage IMHO.

How can also convert one of these VOB files into another file format such as AVI?

Most good free video encoders / converters stopped supporting the old .avi container.

To convert DVD to .mp4 (m4v) or .mkv, I'd recommend Handbrake. You can open directly the folder with the .VOB, .IFO and .BUP files with it.

What's the best program to convert video files from one format to another (i.e. mp4 to avi, etc)?

I am not sure here what to recommend.

To pack something into .mp4 or .mkv digital container format , I'd recommend Avidemux, using the stream copy function. This that repacks only and doesn't decode / re-encode, it is fast and without losses.

To encode (which means losses in quality) into .mp4 or .mkv digital container format, I'd recommend Handbrake again.

There is as well Super from eRightsoft, allowing to convert nearly anything to anything including stream copy functions. It is basically a GUI for ffmpeg. For some reasons I don't like it.

If you really want to have .avi, VirtualDub(Mod) might be an option, but it's user interface is horrible and you need to know what you do (e.g. calculate bit rates manually).

The site http://www.videohelp.com/tools is a true treasure box regarding any video treating tools.