Our billing for Shop Studio Live will happen through Shopify as a monthly subscription charge based on the plan you have selected.
For specific details on Shopify apps' billing cycles, review this detailed resource from Shopify (external link).
To summarize, for your typical Shopify subscription, you are invoiced every 30 days, which is a payment in advance for the following 30 days. Shopify Apps subscriptions are billed with the next Shopify 30-day invoice.
For Shop Studio Live, once your free trial ends, your recurring app charges start based on the price of the plan you have selected.