Gathering Requirements
Brainstorming 
Brainstorming: A group activity designed to generate a large number of diverse and creative ideas for the solution of a problem.
In a brainstorming session there are no "bad" ideas. The aim is to generate ideas; not to validate them. Brainstorming encourages you to "think outside the box" and put "crazy" ideas on the table without fear of rejection.
User Surveys
Surveys can be used to solicit responses and opinions from a large number of stakeholders regarding a current product or a new product.
Observation
Observing users in their natural work environment can uncover product requirements. Usage data of an existing system can also be used to gather information about how an existing system is being used, which can help in building a better replacement e.g. to find the situations where the user makes mistakes when using the current system.
Interviews
Interviewing stakeholders and
Domain Expert : An expert of a discipline to which the product is connected e.g., for a software used for Accounting, a domain expert is someone who is an expert of Accounting.
Focus Groups
[source]
Focus groups are a kind of informal interview within an interactive group setting. A group of people (e.g. potential users, beta testers) are asked about their understanding of a specific issue, process, product, advertisement, etc.
Prototyping
Prototype: A prototype is a mock up, a scaled down version, or a partial system constructed
- to get users’ feedback.
- to validate a technical concept (a "proof-of-concept" prototype).
- to give a preview of what is to come, or to compare multiple alternatives on a small scale before committing fully to one alternative.
- for early field-testing under controlled conditions.
Prototyping can uncover requirements, in particular, those related to how users interact with the system. UI prototypes are often used in brainstorming sessions, or in meetings with the users to get quick feedback from them.
[source: http://balsamiq.com/products/mockups]
💡 Prototyping can be used for discovering as well as specifying requirements e.g. a UI prototype can serve as a specification of what to build.
Product Surveys
Studying existing products can unearth shortcomings of existing solutions that can be addressed by a new product. Product manuals and other forms of technical documentation of an existing system can be a good way to learn about how the existing solutions work.
📦 When developing a game for a mobile device, a look at a similar PC game can give insight into the kind of features and interactions the mobile game can offer.