For people to be able to go to your website, you need to link it with a unique address on the internet - a domain name.
Buying a Domain Name
You are most likely to want a 'generic top level domain', such as '.com,' '.net,' '.org' etc. or country code top level domain such as '.uk,' '.nl,' '.us' etc. You might be happy with a 'second level domain' which may be cheaper to buy, such as '.co.uk,' .org.uk,' '.net.uk' etc. One might be enough, provided the prefix name is distinctive, although you may want to consider defensive registrations as well (see below).
Choose a prefix name (the bit before '.com' etc.) that is the same as/similar to your brand name (see Brand & Marketing and Trade Marks to learn more on choosing a distinctive name that is not already used or registered as a trade mark by someone else).
Try to buy your domain name before registering your company name or trade mark, to avoid being on the radar for potential 'cybersquatters' (see below).
There are various domain name registrars you can use to buy a domain name. They may ask if you want to set up one or more associated email accounts: think about using a service that can offer email services with enough storage and security to meet your business needs (for example to store customers' personal data securely to comply with data protection legislation).
You may want to consult an IT services professional to advise on the best service to choose, but the purchase and registration process itself is fairly straightforward.
Challenging Domain Name Ownership
You may find that someone has already bought a domain name that uses your business or product name. They may have a legitimate reason for doing so (for example a similar or identical business name). If so, there is little you can do - try to find another domain name that is not confusingly similar to theirs but which still associates strongly with your brand.
If you think they registered a domain name in bad faith ('cybersquatting'), you can apply to have the name transferred to you, or cancelled to avoid confusion/negative impact on your brand. Bad faith could be:
Intent to sell to you at an inflated price
To disrupt your business
To benefit from customer confusion with your brand to steer traffic to their site for financial gain
Ownership disputes are usually resolved via the arbitration service of the relevant domain name registry: much cheaper and quicker than going to court. However, claims are usually made on the basis of relevant trade mark rights: engaging an intellectual property lawyer will help you to make the best case and improve your chance of succeeding with your claim/defence of ownership.