If you can be physically present while the user performs his tasks, mainly focused on behavior:
- fly-on-the-wall technique ('shadowing'): simply observe, no interaction, no questions during the task (afterwards is fine). Allows you to see real-time behavior in a natural setting.
- contextual inquiry: a situated method where you ask questions while the user is performing a task in its natural context. It's a bit more intrusive than pure observation, but can lead to fruitful conversations.
If you need more insight into people's thoughts, emotions and subjective experiences rather than their behavior:
- experience sampling: at regular intervals, or in response to certain events, you ask your participants for a reaction (such as describing what they're doing, how they're feeling, filling out a questionnaire, or taking a picture).
- diary study: participants keep a diary recording their activities and experience. The main difference with experience sampling is that with diary studies the participants can choose the moments when they want to work on their diaries
For specific questions or hypotheses it can be wise to work outside the natural settings. For example if you need to find out the error rates caused by working on a moving vehicle, put your participants on a moving subway. If you expect there could be much distraction during use, make sure you distract your users during using testing by having them perform a secondary task simultaneously. Or simulate an extremely high event rate.