Download and burn to disc is the easiest path. There does exist an installer for Windows, but it won't result in a full featured install, and will generally result in a less stable system. So just burning a CD is the "standard" way. If you have a few GB of space on your hard drive, the installer should be able to just resize your windows partition and install Ubuntu on the free space.

Re: accessing Linux file systems from Windows: there exists a Windows driver for ext2 file systems, and I think two file managers that will do the same. As far as I know, none of them have decent write support. Your best bet is to either dedicate a partition to shared data and format that in FAT (or NTFS, which will need a little tinkering, but nothing too hard), or to use external drives for sharing data between the systems. On my one system that still contains a WIndows installation, I have a FAT partition and link to them from my home folders. Of course it comes with all the disadvantages of those file systems. With FAT you have no security whatsoever. With NTFS you rely on a poorly documented file system. For instance, you won't be able to access the data on NTFS partitions after hibernating your Windows system.