If you decide to buy shares online, then the easiest thing to do is open what's called a 'nominee account'. This allows you to own shares without becoming involved in any of the paperwork.
Often, this account's known as a general investment account (GIA). You are still the legal owner of the shares, but your name will not appear on the company's share register.
You can also hold your shares in a Stocks & Shares ISA or a Self-Invested Personal Pension (SIPP).
While you're holding your shares, it's important that you don't forget about them. When you're new to investing, the excitement of it all may mean that you keep an avid eye on how your shares are performing.
However, as you build your portfolio up and invest in more shares, it's easy to let things slide, so make sure you keep a track of everything you've got by reviewing your portfolio regularly.