Understanding and being familiar with the data sources as a whole is the first step, requiring reading and re-reading the data, until it is clear to the researcher what concepts, issues or topics are common or vary across the corpus of data. Some researchers believe this is the only necessary process, especially with small data sets with an individual researcher. However, there are other methods to adopt.
Some possible approaches include thematic or content analysis, Discourse analysis, Narrative Analysis, Semiotic analysis, In-vivo coding or Interpretive Phenomenological Analysis (IPA). In a sense, these are all different ways of reading the data, looking for different patterns or trends.
In general, most approaches to qualitative analysis work with any type of data, so you can use them for analysing interviews, focus groups, diaries, documents, social media or other sources. Most original research focuses on creating or recording dialogue from respondents, and regardless of whether these sessions are recorded with audio or video, text is usually the main focus of the analysis. Although useful context can be gained by listening to the nuance of how people talk, or watching their gestures, most analysis uses text transcripts to guide the analysis.
In questionnaire research, qualitative analysis is important for understanding the open unstructured text elements of survey questions. This may also be combined with responses to discrete or quantitative metrics - this is referred to as mixed-method research, which combines some elements of both quantitative and qualitative data and analysis.