Meta Tags
A long time ago, meta tags mattered a great deal. Today, the idea that everybody on the internet is going to be truthful and honest about what's in their html documents is laughable. There's literally thousands of dollars at stake.
When meta tags did matter, AltaVista and other older search engines soon found people using them to make large fictitious claims about their content in order to get more traffic. Adding or changing your meta tags won't give you a magical boost in search result ranking as they just aren't given much weight.
On the other hand, providing relevant and informative meta data about your website is not a bad idea. Truthful reporting of your web page's content can even do you some good. Google often uses the description meta tag as the text blurb next to the link it shows in the search results. As well, Google's Adsense program uses the meta information as part of how it determines what ads to show. Not stretching the truth about your pages in both cases can lead to a better click through rate (CTR) for you and a better click through rate if you use Adsense ads.
The last usage for them is to list the alternative spellings or common mistakes made when spelling your keywords that you would feel embarrassed actually typing in the page text. Whether American spelling should be classed as a spelling mistake is a matter of personal opinion.
Valid Meta Tags
XHTML:
<meta name="keywords" content="pike, place, seo, optimization, optimisation, tactics" />
<meta name="description" content="Pike's SEO Tactics - Internal" />
HTML:
<meta name="keywords" content="pike, place, seo, optimization, optimisation, tactics" >
<meta name="description" content="Pike's SEO Tactics - Internal" >
An interesting point is that valid HTML meta tags have no closing tags and no final slash.
Keywords
Choosing the correct keyword combination for your website is all about understanding what your users are searching for. If you're a small website with few links then you are highly unlikely to rank highly in search engine results on broad terms like "travel" (Google - 233,000,000 hits). Ranking well on a more specific search like "travelling with dogs" (Google - 530,000 hits) is a managable long term goal.
The Overture keyword tool or Word Tracker can give you an idea of how many people are searching for a combination of keywords. A tool which combines the results is available at Digital Point.
The last usage for them is to list correct alternative spellings (like American or British), alternate words used in different dialects or common mistakes made when spelling your keywords that you would feel embarrassed actually typing in the page text.