To build up answer/solution during interviews:

1. Start with the brute force solution. It shows you understand the problem.
2. Think out loud Always. 
3. Write your own 3-5 test cases.
4. Write all the steps you are going to follow in your approach. It makes things easier for interviewer to follow along your approach.
5. Start coding and Refer back to each step of your algorithm.
6. Dry run your code line by line against your test cases.
7. Check with the interviewer if you need to walk them through your approach.
8. Tell time and space complexity of the solution. 
9. Offer to optimize the algorithm. Point out the inefficiency with first approach then explain what you can do differently.

Hope my answer helps you. if you have any other doubt, please reach out to me. 

DSA is an aspect most often considered by companies when evaluating problem solving skills of an individual. But just being good with DSA is not sufficient enough, we need to consider different other aspects while being in interview. Few of them in order are-

• Clarifying question asked by interviewer.
• Coming up with a brute force approach first and have a small discussion on this solution and time and space complexity.
• Optimising logic to bring solution under given constraints.
• Keep speaking throughout what's going on in your mind.
• Ask for hints if stuck for long.
• Discuss the solution and T&S complexities with interviewer.
• Code it, make sure it's clean and readable.
• Do good testing of it, make sure you are not missing any edge cases.
• Ask interviewer to review your code.
• Ask some questions to interviewer about company/product/tech stacks.

Avoid asking for feedbacks at end of company interview as it is supposed to come via HR.

Above discussed points are for DSA interviews, there are certainly different aspect to be considered for Machine coding/Hiring Manager/ Design rounds.