Since 10.6 will run in 1GB of memory, sometimes called RAM, I assume you mean you only have 1GB of free space left on your hard drive? If correct, see this FAQ: http://thexlab.com/faqs/freeingspace.html
At the Apple Icon at top left>About this Mac.
Then click on More Info>Hardware and report this upto but not including the Serial#...
Model Name: iMac
Model Identifier: iMac7,1
Processor Name: Intel Core 2 Duo
Processor Speed: 2.4 GHz
Number Of Processors: 1
Total Number Of Cores: 2
L2 Cache: 4 MB
Memory: 6 GB
Bus Speed: 800 MHz
Boot ROM Version: IM71.007A.B03
SMC Version (system): 1.21f4
Open Activity Monitor>Disk Usage tab, Show:>All Processes, sort on CPU%, how much Free Space is used?
On This Site It Tell You The Specs For Snow Leopard >> http://www.apple.com/macosx/specs.html
In General Requirements, Second Bullet Point Down It Says 2GB Of Memory And Im Guessing That Is Talking About What Is Said What You Click 'About This Mac' And It Tells You About What Processor You Have And The Memory, Mine Says 1GB For Memory. Is This The Problem?
Yes, that will prevent it, in fact I don't think you'd be happy with the minimum 2 GB of RAM.
Lion/101.7 System requirements
• x86-64 processor (Macs with an Intel Core 2 Duo, Intel Core i3, Intel Core i5, Intel Core i7, or Xeon processor.)
• At least 2GB of memory, (I say 4GB)
• Latest version of Mac OS X Snow Leopard (10.6.8), with the Mac App Store installed
• At least 4GB of disk space for downloading, (I say 40GB at least)
Like Snow Leopard, Lion does not support PowerPC-based Macs (e.g., Power Macs, PowerBooks, iBooks, iMacs (G3-G5), eMacs).
Lion also does not support 32-bit Intel Core Duo or Core Solo based Macs. Rosetta is no longer available in Lion, which means Lion no longer supports PowerPC applications.
Then I'd go for the 8 GB kit...
There are installation videos here for the 4 2009/2010 Mini models...