Before you get started, make sure you have all the requirements available: server space at a hosting providedprovider, domain name, FTP client, text editor. Makes sure to follow the instructions in the "What you need to get started" page first: http://doc.prestashop.com/display/PS15/What+you+need+to+get+started.
Some web-hosts offer a 1-click install in order to save you time and get you started even faster. Those web-hosts mostly use the following script libraries:
Using these can drastically reduce the installation time for inexperienced users. Some of these scripts even support 1-click update, which is invaluable.
Other hosts have their own installation scripts. Check with your own host for more information.
FinallyLast but not least, PrestaShop has its own hosting solution: by registering on PrestaBox, you offload all the technical hurdles of hosting to our own team, and can focus on your shop, clients and sales. Visit https://www.prestabox.com/ for more information.