For starters, they would need their current government to agree with that plan.

Or they would have to declare independence while their government is actively engaging in genocidal policies against them.
In that case, this fact needs to be widely recognized. They might even receive international help for their struggle.

Another option is declaring independence when the previous country is already falling apart.

In any case, for a successful declaration of independence, the group seeking independence would need to be a distinct ethnic, religious, or linguistic community that lives in a specific region and is a majority in that region.