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 or services rather than simply company names. The idea is that people trying to find things online will be able to locate a business website without the prior comprehension of the business or its name. You will find all manner of tricks and techniques which fall under SEO, but the good sustainable methods (also sometimes called "white hat SEO") are based around the perception of making your web site easier for search engine to read and understand, meaning they rank you higher in searches for appropriately relevant terms.
It's not uncommon to decide to outsource SEO to external
digital marketing agencies and other companies, but there are actually far too many dodgy types available who like to take companies seeking SEO - especially local and smaller companies - for an extremely expensive ride. How then does one actually go about finding the best, honest and legitimate search engine marketer?

It really is actually incredibly easy to seek out a decent SEO agency online. Go to a search engine like Google or Bing and type in "SEO agency." Ignoring the paid ads 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 own website would not be so high in the natural listings!
To narrow things down a bit, you may try extending your search. Say you live in Essex and want a local agency - just type in "SEO agency Essex." Or if perhaps your web site is specialised and you want particular help with it you can add your industry or site type - "SEO tourism" or "SEO eCommerce" for example. This could be a great way to search out 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 business 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 great. The exact same is true of SEO services advertised on paid ads at the top of internet search engines or on banner advertisements on other websites. If their search marketing is any good, why are they having to pay for their placements?
Something else to bear in mind is to steer well clear associated with any SEO agency that promises you "top position for x keywords" or something similar. Virtually all modern search engines used personalised searching, meaning that everybody sees sites in slightly different ranking positions based on their personal search history. Absolute rankings are a thing of the past, any anyone claiming to deliver this kind of service is lying through their teeth. Modern SEO shall use sustainable "white hat" techniques so that you can bring useful traffic to your site, not use exploits and dodgy tricks, that can 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 will need to ask them some questions before you leap into their services. And also the usual checks like existing client list and testimonials, it is a wise idea to speak to someone directly on the telephone or even in person.