Hi Adrian, done a bit of housekeeping, added your twitter link to your profile and your image as your avatar.
As questions go, this is the $64 million one
How to get exposure.
There's two ways of doing it, ones pretty straight forward, and one is lot more hard work, but can be done with some serious effort and dedicated time.
Option 1 - Marketing Budget
Most new business ventures plan out some kind of marketing budget. "Build it and they shall come" philosophy rarely works, and tends to be you can build it, but we don't really care 
So you have to make people care, which is what marketing aka exposure etc is all about. The bigger the budget, the easier the task and vice versa.
Small Budget - Concentrate on a small professional looking website. Wordpress or similar will be adequate, pay someone a couple of hundred quid if you can't do it yourself. This can then be your base from which to promote. Blog pages, articles, sales landing pages etc. Wherever you promote them, you will send targeted traffic back to your website, which will give reassurance.
Any left over pennies, use it where-ever you have skill gaps. I'm assuming proof reading and copy isn't an issue for you, but is for a lot of people, so that's a cheap thing to outsource. If there are any areas you are not comfortable, then seek out 3rd parties from the likes of forums and communities like this. If you can afford a small PPC campaign, this could give you a good insight into your target market, the kind of keywords which work for you. You may find Facebook PPC is as good or better than Google due to the way you can specifically target an audience.
Big Budget - Ideal world, outsource to an agency and concentrate 100% time on running your business and servicing clients.
Option 2 - No Budget - most new businesses reality 
Remember your time is also a budget. Spending all day marketing means less time running your business, so always factor yourself in to any budget decisions (unless you work for nothing
)
No budget makes life harder, but not impossible, and plenty of businesses have prospered after little investment. But this is the hobby business category, so its down to available time and what skills you have, or can beg borrow or steal!
IMHO having a professional website presence, albeit just a few page brochure style, is essential. Wix and other free website builders just give the wrong impression, and send any hard earned targeted traffic in search of your competitors.
Just my 5 pence worth, doesn't mean I'm right.
Finding leads, punters and targeted traffic
Once you have a platform that is likely to convert visitors into genuine leads or conversions, the next trick is to find them!
For a new business, and particularly a service type business (versus flogging widgets), then the most effective way of people finding your service is for you to become an known expert in your field. Maybe you will strike it lucky and get some great search engine optimisation, and be at the top of Google for your chosen search phrase. But if you're not, becoming known as an expert will help you get there as people start linking to your content, posts, blogs etc.
Forget hard sell, go for soft sell. Eg this forum, in your signature you can put a bit of blurb, but as you post in the community, you will become known as the English Tuition bloke. Now replicate that across a few forums, and you are starting to build a reputation.
Get active in a relevant Facebook group. If one doesn't exist, start one. Likewise, Google Plus is now very big and pushing user communities. Find one and get active. You may find a local "all things Surrey" one. Join that and become known, it's then good old word of mouth.
It's a hard slog, but if you have the time and motivation, service style businesses can use social media to their advantage. Just remember the name, "social media" and be social. Most people fail because their facebook pages are a sea of self promotion and sales, which no one is reading apart from them.
But as you start, keep analysing results. Use Google analytics on your website (it's free) and will give you a gold mine of info. If a platform isn't working for you, ditch it and move one.
Guest publications is another good avenue, write some really professional and creative content and their are plenty, quality decent sites out there that would host it. Quality is key, people will say guest blogging is dead, Google doesn't like it etc etc. It's all cobblers. Google wants quality content, so provide it, and put it on quality platforms.
That's scratching the surface, but hopefully provides a good starting place.
Anyone else got any good suggestions, or agree disagree?