I wonder if anyone could explain how a website appears high on search results?

Hello, Im building a website for my wedding stationery business using Mr.Site.but I only have a limited knowledge as to how the internet actually works.
When I search a subject such as wedding stationery, why do the same online shops keep appearing on the first result page, no matter which search engine I use?
Do you have to pay a fee for this service, or is it the number of hits a site achieves.

To make your website appear high on search results is called the Search engine optimisation (SEO) which is a technique of Online Marketing. There are millions of companies all across the world who offer SEO services. These companies analyse the Vertical that your website runs on, analyse the competition, the keywords, the website design, exchanging links and many more things. It normally takes around a minimum of 6 months from the time your website goes live to rank high in the SERPs (Search Engine Result Pages). For these 6 months, a regular monitoring of the site is needed.
There are two ways that you can actually follow to get higher ranks on SERPs - Organic optimisation and Paid Optimisation.

Organic Optimisation is where you do not pay anyhing to the Search engines but optimise your website organically complying to the algorithms of the Search engines and the results are visible only after a minimum of 6 months.

Paid Optimisation is the process where you pay to the Search engines for getting a higher rank and there is a separate space for the Paid results on the SERPs. The sponsored links when you google on your right hand side are a result of the Paid optimisation.

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You pay to have your site come up first. This is how they make their fortunes!

If you do your own HTML you will know about embedding tags and keywords into code on your index (or other pages).Search engines pick these up and thereby get some idea of the site's content.

How the engine ranks your site compared to others depends on what search algorithm(s) it uses.You would think that a search engines rank similar sites by order of how popular it is & how many hits it receives.But Google apparently ranks highest sites with the most links to other sites on them.So there is no one answer..You have to investigate search engine by search engine.You can pay some search engines to give you a higher profile on their site and there are also companies who claim to be able to get you a higher ranking for a fee but I have no experience with them.