Quality is delighting customers
You have few choices:
If there are no requirements, work to prepare the required documents.
If there are no requirements, understand project from business teams and development team and start working.
regarding model, you can choose any model you want if your PM has no clue what model to approach.
you can start process and approach and provide a demo and make them to understand and give advantages and disadvantages. I am sure, they will like it.
Based on my knowledge and experience
If the client is not sure about wht he wants
Then go for the model Prototype
I don't know what you mean by "model" -- perhaps you could give some examples.
There are always requirements, but they may not be written down. If there is a requirements document, it is rarely complete or accurate. And of course requirements change over time. Just because it was complete and accurate when it was written does not mean it is complete and accurate now. Mostly likely, everyone on the project works from a different set of requirements that reflect when they joined the project, what they are working on, and what interests them.
Nonetheless, part of your job as a tester is to understand the requirements as best you can. If nothing is written down, you can start by "playing around" with the product, writing down questions as you come across things that you don't understand, and then following up with people on the project to answer those questions. You may never get back to the original business requirements. Sometimes it's ok to say, "I don't know how to test this against the business requirements because I don't know what they are, but I can still test the implementation."
Hmm, yes sometimes situation arises that the tester has work on a previous project which didn't have any requirements document or sometimes the clients becomes so hurry that documentation preparation couldn't make out.
In that case, the Tester has to be strong enough on his domain testing area. For that tester should meet the domain expertise or will make frequently client conversation.
Thank you for various inputs.
More specific in terms, You have the application/project/software which is ready for testing and there are no requirements to test a project/application/Software. How do you assure the application/project/software is stable? Which SDLC model is best suited in this case?
And when does agile model/methodology comes into picture?
By "stable", do you mean "high quality" or do you mean "no longer undergoing significant changes and now ready to be tested"?
If you were using Agile, you would know the requirements.