How to choose a good domain for my website?

[livewyre]

Not all the advice you will get is actually good SEO-related advice.
For instance choosing your company name as a domain name is excellent if your brand is already known by the clients/visitors you want to reach, but if people don't already know your name, it is a good idea to use a keyword in your domain. Your company name does not need to be in your domain at all from an SEO perspective.
Using dashes as word separators is fine and may get you a domain you want IE:
You may find jewelerynewyork.com is taken but jewelery-new-york.com is available...
You don't need to keep the domain name really short, you may need to be prepared to take a longer domain name to get one that fits your purposes - this is fine (as long as you don't go ridiculously long..). You may also consider .net instead of .com..
Think about how you can use the key search terms that you imagine people who will want to visit your site will use. IE. if you are providing a local service, you should use a geographical location in your domain cakesinaspen.com for a store supplying locally to Aspen.
I don't know if you are looking to make a commercial site or personal site or information site otherwise it would be easier to give more specific advice.