Well done search engine optimisation, often called SEO for short, is designed to allow web sites to show up in search results when people look for products rather than simply company names. The idea is that people searching for things online are able to seek out a business website without any prior comprehension of the business or its name. There are actually all manner of tricks and also techniques which fall under SEO, however the good sustainable methods (also sometimes called "white hat SEO") are based around the concept of making your webpage easier for search engine to read and understand, meaning they rank you higher in searches for appropriately relevant terms.
It is not uncommon to decide to outsource SEO to external marketing agencies as well as other companies, but you will discover far too many dodgy types around who like to take companies seeking SEO - especially local and smaller companies - for a really expensive ride. How then does one actually go about finding a great, honest and legitimate search engine marketer?

It is actually incredibly easy to seek out a quality SEO agency online. Go to a search engine like Google or Bing and type in "SEO agency." Ignoring the paid advertisements at the top, whichever firm has landed at the top of the search results are what you want - they has to be very good at SEO or their very own website wouldn't be so high within the natural listings!
To narrow things down a bit, you could try extending your search. Say you reside in Essex and want a local agency - just type in "SEO agency Essex." Or if your web page is specialised and also you want particular help with it you can add your industry or
Recommended Resource site type - "SEO tourism" or "SEO eCommerce" for example. This could be a good way to locate niche SEO agencies who have specialist knowledge in your field.
Sometimes SEO agencies (or at least people claiming to be SEO agencies) try and solicit companies by sending them emails or submitting contact forms with various enticements and offers. However if you see something like this come in then it is best to ignore it - if a company which supposedly specialises in search engine optimisation is reduced to spamming inboxes to get business rather than, say, doing SEO so their very own website ranks highly and people can find them anyway, chances are they are not very good. The exact same is true of SEO services advertised on paid advertisements at the very best of internet search engines or on banner ads on other web pages. If their search marketing is any good, why are they having to pay for their placements?
Something else to keep in mind is to steer well clear of the SEO agency that promises you "top position for x keywords" or something similar. Virtually all modern internet search engines used personalised searching, meaning that everyone sees websites in slightly different ranking positions according to their personal search history. Absolute rankings are a thing of the past, any anyone claiming to deliver this sort of service is lying through their teeth. Modern SEO shall utilize sustainable "white hat" techniques in order to bring useful traffic to your website, not use exploits and dodgy tricks, which could constantly get them slapped by search engine updates like Google's infamous Panda and Penguin algorithm changes.
Once you have found an SEO company that looks mostly all right you certainly will need to ask them some questions before you decide to leap into their services. And the common checks like existing client list and testimonials, it is a great idea to speak to someone directly on the phone or even in person.