Keep in mind that your brand will become known for the highest quality your customer is willing to accept for the lowest price.
Small businesses should try to differentiate themselves on other aspects of their products or services, e.g., more unique selection or extensive of products, longer or better-suited hours, more personalized service, less staff turnover (and therefore more continuity of service), ability to respond much more quickly to whatever is going on in the local scene/market, other added value bits and pieces to tack on, etc.
The small local IT support company will better get to know your business or home computer network than a large chain. A small clothing store (mortar and brick or online) might source more interesting manufacturers of unique blouses. A local bakery might reach out to local charities about donating leftovers, which could lead to nice press.
Since you cannot necessarily compete on price, find a niche. That niche would be an area of specialty products or services the big guys do not offer.
Not only do I have little interest in the boring apples the supermarkets always carry, I have less interest in taking up space in my garden to grow those same apples. Offer me a young apple tree that does not produce the same kinds of fruit I already find easily at the market.
Excellent customer support with human touch will help you, the big guys always work on a number basis. At the end of the day only numbers matter to them. But, for small businesses like you and me, customer satisfaction is very important.
How many big companies make a post sale call to customer? After you sell something, just call the customer and ask whether they are satisfied with the product/service. If not, discuss the problem and sort it out. If you offer any free services, do not wait for the customer to give you a call and ask you to visit for a service. Many forget to use their free services and if you follow up and do it, I am sure your customers will be very happy with your company. There are small things like this which will make them happy. And they will recommend you to others and price will rarely matter to them.
Bottom line...don't compete on price. Ever!! It's a loosing proposition. A client can always find someone to undercut your price. So just drop the idea all together.
Consider a few things...
USP - what is your Unique Selling Proposition? In other words, what makes your business unique? What combination of skills and service can you bring to a client's project? They're there if you look.
Benefits. Always focus on the benefits of working with you. And have answers to the questions about 'the other guy.' Doesn't matter who they are, you should be able to say, 'most people in my industry operate this way. but not us, we do it that way and here's why.' This goes back to USP.
Results. If you're selling B2B then have projects where you've helped your clients get real-world, bottom line, measurable results. Nothing says it louder than 'the new website we designed increased traffic 100%, signups 300% and customer conversions 120% 90 days after launch.' If you can highlight the results of working with you, then price most of the time goes out the window.
Support. Provide the best possible customer experience they could ever have. Make it public. Use social media to display your customer service - not by bragging - but by having service conversations in public. And encourage your customers to share their experiences.
Referrals. The cornerstone of any business. There will never be a better marketing approach then having your past clients send their friends and colleagues to work with you.
References. Take a few past clients who loved your work and ask them to be references for future prospects. Ask up front, get their best contact details and coach them a bit on what they should say. Draw out the benefits and results from them so they're thinking about it when your prospects get in touch. And, help them highlight those intangible experiences they really loved in working with you. Stuff you don't know about until you have that conversation. But it's the stuff that makes your USP even stronger.
I could go on but that's probably enough. As you can see, there's lots of tactics to use that have nothing to do with price.