SaaS application development is not much different from traditional development methodologies. The biggest difference is incremental progress, constantly testing the market, finding the product market fit, and evolving the product and most saas application development services are built around that.
The key steps a SaaS development company would follow to build a SaaS application are as followed:
Planning and documentation
Wireframing and SaaS software design
Development of the SaaS product(Front-end and back-end)
Quality testing and performance testing
Deployment on live servers
Performance monitoring, maintenance and support