You have to buy Virtual Machines from DigitalOcean or AWS inorder to host your laravel app. In DigitalOcean VMs are called 'Droplets' and 'EC2 instance' in AWS. The pricing of DO droplets starts from $5 per month (1GB ram, 25GB ssd). For a Laravel app without huge traffic that should be enough. If the traffic increases you can upgrade in future. digitalocean.com/pricing
Aws also have similar plans. But they're generally 30-40% costlier than DigitalOcean. See aws.amazon.com/ec2/pricing/on-demand