Downloading the iso will not affect your computer.
You may need software to burn the CD, see
In addition, you can use unetbootin to use a flash drive rather then a cd if you wish.
When booting the CD / USB you can try Ubuntu and test your hardware. Again, bu default it will not affect your computer, although it could if you do something without understanding what you are doing.
If you wish to install, see https://help.ubuntu.com/community/GraphicalInstall
Be sure to back up your data first . Although data loss is rare, it can happen.
In addition, be sure you understand partitioning.