Shopify is mainly built around products, which means if you are hoping to sell one to one (or one to many) type services it can get a bit tricky. But it can be done and I'm going to take you through a few options now!
One is to use an app from the --> Shopify App store. There's one in particular --> called Sesami which works quite well. If you are a one person team and have one type of consult that you offer then it is completely free to use. To avail of further benefits you would need to choose which plan suits you best. Here's a little snippet of other plans available
One of the benefits of using an app is that it is all built into your shopify admin and storefront. Your customers can pick a time and date that suits them, then pay for it in the normal way of adding it to their cart and going through the checkout process. Any payments that are taken will also be processed through Shopify - depending on which Payment Gateway you use (Shopify Payments, Paypal, Revolut etc).
Another option for allowing your customers to book online with you is by using a third party booking system --> like Calendly for example. You can use your website to talk to your customers, share informative (or fun!) blogs, build an "About" page, and share opening hours/shipping details. You can then link in a little bit of code from your Calendly account and voila, there's a calendar on your website ready to use. If you use Calendly for payment (as in your customer books and pays via calendly), you will need to have a payment option linked up there (stripe/paypal etc) within your Calendly settings.
Another option here is to have your customer pay for a consult with you on your website, and then have the link to your Calendly calendar sent to them automatically. This means they won't get to book until after they've committed to the consult, and payments are all taken care of through your Shopify account. If you'd like to find out more about pricing you can --> do so here. (there is also a free option here for one type of consult).
This isn't a complete list, however hopefully it gives you some food for thought! Any questions, send me an email or comment below. I'm currently building out similar websites for clients so I'm more than happy to take this task off your hands. Talk soon!