Do you currently have a makeup services business? Ultimately I would start by thinking about your target audience, and where they go to find information on Makeup services.
We know they are likely women, what age are they, in which city/areas do they live, how do they spend their time, which magazines do they read, which websites do they visit, how do they spend their time on social media? If you can gather this information (ideally using data from your existing business, or by creating a short interview guide to ask prospective customers) that will help inform how do develop your marketing strategy and guide your marketing mix.
I would create a persona of this ideal target customer, and then based on the information above make decisions on whether you want to advertise on social media, magazines, use PR, partnerships, events etc.
I’d also ensure you have a solid web presence with a good website, and the ability for your clients to book online. Your website should contain information about the services you provide, what makes your business different from others who provide Makeup services (your unique selling proposition), and ways to easily understand your schedule and make an appointment. It should of course also contain information on where/how to find you (your address), opening hours etc, and any other information that you think will be helpful to your clients (ie nearby parking etc).
If you conduct interviews with prospective clients I’d ask them what keywords they use to describe your services, and ensure thesee are embedded in your website so it is search engine optimized (your SEO strategy). These keywords are likely also going to be useful to you in a paid search strategy, so that when customers google “makeup” “makeup for my wedding” etc your site comes up in the top search results.
I hope this helps~