Puppy Linux has many versions, you can visit puppylinux.com, the official site, and find lots of information there. Also, check the Mainline Puppy Linux Distros and Puppy Derivatives topics in this forum.
For best results, it's important for you to match the Puppy version to your computers hardware capabilities.
Puppy's come in 32bit and 64bit (newer) versions. This refers to the CPU's ability.
General hardware minimum system requirements are:
CPU Type = x86, x86_64, AMD64
32bit Puppy's - CPU = single core Pentium 4 or equiv, RAM = 512mb
64bit Puppy's - CPU = 64 bit dual core, RAM = 1gb
*NOTE - 64bit CPU's can run 32bit Puppy's, however, 64bit Puppy's have the best internet capabilities.
If you are unsure about your specifications try booting your system and entering the bios setup during boot (check the internet for how to do this or ask a computer friend to help). Your CPU and RAM information should be contained there. You can also try checking the internet for your make and model, which can give you a general idea.
Last, since 64bit computers can run 32bit Puppys, you can download and run a 32bit Puppy and use that to determine the CPU and RAM.
There are many users running Puppy with less hardware than listed above, but they do so at the cost of performance and usability, particularly related to web browsers and internet access. This is a fact not only for Puppy Linux, but also for Microsoft Windows and Mac's. It is dictated by today's web standards.
Recommended Puppy versions - Read the topic Making a CD or USB for your First Boot
Need more help? Join the forum and post your questions in Beginners Help.