I apologise for the incoming wall of text but there are multiple solutions to your problem and not mentioning them all would not sit well with me. One of the nice and simultaneously annoying things about linux is there are usually alternatives for everything you might want to do.
If you just want to try it out and have a reasonable amount of ram (vista minimums* should be OK) then you can run a liveCD for quite a while and get the idea behind it all.
Still if you do want to dual boot then you are going to have to do a few things.
Linux does not tend to opt for NTFS as a base file system and this includes ubuntu (you can easily access the data on it though) so you are going to have a few choices to make
There is a so called virtual file system type thing called wubi
https://wiki.ubuntu.com/WubiGuide (various other distributions have similar features named different things, indeed some of the full on liveCD type distributions like puppy linux are built around it) that you run from windows and it can load/read from that. It is not ideal and probably not quite full speed and it is a bit cumbersome to tweak but it works.
The other way is to go the more traditional route and partition your drive to accept linux. As mentioned NTFS is not the chosen file system for most linux distributions but you can snatch space from it and give it to linux.
This is where it can get a bit tricky (especially if files are fragmented badly) but the outline of it all is simple enough.
Linux can run on one partition but most have two or even three depending on how they want to play it.
1) The main partition
2) The swap space (virtual memory, page file- all the same idea). You can run without it but it is not that wise on linux- kick a gig to it.
3) The home directory- not all people do this (in fact I would probably say most people new to it do not do it as it is mainly people that shift between distributions or reinstall a lot that do it)
As you asked for a step by step to resizing
http://gparted.sourceforge.net/larry/resize/resizing.htm
If you already have the partitions there the installer should give you the option of picking what goes where. When you boot into a liveCD there is probably a program called gparted (again multiple things for the same task)- this will be able to shrink and resize partitions to do what you want.
Bonus info- you vista home basic which screams vendor machine to me (made by HP, dell, sony or the like). These last few years they have been cheapskates and instead of pressing some discs kicking a portion of the hard drive to a "recovery partition". Nothing stopping you from grabbing that and using it for linux.
*I am fully aware of how low some makers go in the ram stakes, even then it should be OK still)
Anyhow during installation you will probably be offered to install something like GRUB although it might be lilo (alternatives again). No real problem what happens as you will get a screen to choose which OS you want to boot (you can customise it to autoboot whatever you like as well if you want).
