Google and other search engines have changed the way they search and you simply have to design what they want to see or not be found. The link below goes to Google's own 'Search Engine Optimization Starter Guide'. Simply download it and read through it yourself. If you are building your own website follow the advice very carefully. If you have a web developer, go through it with them to check that they really have done everything they need to do. If you have a website already review it or go through it with your developer.
Lastly Google like active sites, with good links in and plenty of unique text and content. This is probably going to be up to you.
It used to be of great importance to register your website on as many directory sites as possible in order to boost your search engine rankings. However search engines will generally now find you quite quickly but will need links to your site from other established websites, social media and lively blogs more than ones from traditional directory sites. Your ranking and search visibility will probably come from these as much as anything.
All this said you may just simply need to be available on the internet. In which case here is a list of websites you may well be able to have a listing. Just click below to either open the document in Word or save it onto your system.