What are the procedures to follow to obtain a visa that will enable me cross-overthere for the master and PHD Programe?

They'll vary based on where you're applying.

This is a guide for visa rules for LLM students studying the US:

https://llm-guide.com/articles/us-student-visas-for-llm-students

... rules should be similar for most other master's programs. Rules for those enrolling for PhD programs may be different.

Here's a similar article for international students studying in the UK:

https://llm-guide.com/articles/uk-student-visas-for-llm-students