Well you have to have at least 2 partitions for Linux.
1. is the 'root' partition and
2. is the 'swap' partition.
The swap in Linux works about the same as it does in Windows, but instead of having a a swap file you have a swap partition.
You have to have about 10 gigs or so for a comfortable root partition. You can get by for a lot less, but keep in mind you need room for your user's files and such.
The swap partition can be much smaller. 512megs to a gig is fine. No need to have it bigger then 2gigs.
As for automatic, resize, vs manual.
Automatic is letting Ubuntu do the default setup for your system. It tries to 'guess' the best settings for you, which may or may not be what you want.
Resize is when you resize the Windows partition to make room for Ubuntu partitions.
Manual is when you manually choose partition sizes and such things.
The key thing is that whatever you choose, just realy be carefull about not letting it delete or format the Windows partition.
Anything else can be recovered from. For example if you want to get rid of Ubuntu you can use the Windows recovery console in the Windows cdrom to restore the Windows bootloader. But if you delete the data off of the Windows partition you can't get it back.
It's worth your time to take a look over things like
Ubuntu documentation:
https://help.ubuntu.com/6.10/ubuntu/desktopguide/C/index.html
User provided documentation:
https://help.ubuntu.com/community/
Unofficial Ubuntu guide:
http://ubuntuguide.org/wiki/Ubuntu_Edgy
For example in the Installation notes for i386 I found this:
https://help.ubuntu.com/community/Installation/I386
If you do not want to erase an entire disk, or if you want to customize the partition layout, choose "Manually edit partition table" from the menu, and the next screen will show you your partition table, how the partitions will be formatted, and where they will be mounted.
One thing to be aware of is that Ubuntu releases a new version every 6-8 months or so. So documentation may be for a different release, most of the time though it's pretty accurate irregardless.
Reading through that fairly quickly, just skimming it over, will probably be helpfull. These things cover common questions and solutions to common problems and that way if you have a good idea were to find answers and terminology (like what do you mean when you say "Do you have multiverse repository enabled?") will probably make things much easier.