There are lots of different ways to understand the contexts and needs different audiences bring to your offerings. You probably also want to test to see if what you're making works for them and to get a sense of what they're currently doing with your websites, apps or venues. It can help to think of research methods along scales of time, distance, numbers, 'density' and intimacy. (Or you could think of it as a journey from 'somewhere out there' to 'dancing cheek to cheek'...)
'Time' refers to both how much time a method asks from the audience and how much time it takes to analyse the results. There's no getting around the fact that nearly all methods require time to plan, prepare and pilot, sorry! You can run 5 second tests that ask remote visitors a single question, or spend months embedded in a workplace shadowing people (and more time afterwards analysing the results). On the distance scale, you can work with remote testers located anywhere across the world, ask people visiting your museum to look at a few prototype screens, or physically locate yourself in someone's office for an interview or observation.
Numbers and 'density' (or the richness of communication and the resulting data) tend to be inversely linked. Analytics or log files let you gather data from millions of website or app users, one-question surveys can garner thousands of responses, you can interview dozens of people or test prototypes with 5-8 users each time. However, the conversations you'll have in a semi-structured interview are much richer than the responses you'll get to a multiple-choice questionnaire. This is partly because it's a two-way dialogue, and partly because in-person interviews convey more information, including tone of voice, physical gestures, impressions of a location and possibly even physical artefacts or demonstrations. Generally, methods that can reach millions of remote people produce lots of point data, while more intimate methods that involve spending lots of time with just a few people produce small datasets of really rich data.
So here are few of my favourite things: analytics, one-question surveys, 5 second tests, lightweight usability tests, semi-structured interviews, and on-site observations. Ultimately, the methods you use are a balance of time and distance, the richness of the data required, and whether you want to understand the requirements for, or measure the performance of a site or tool.
Analytics are great for understanding how people found you, what they're doing on your site, and how this changes over time. Analytics can help you work out which bits of a website need tweaking, and for measuring to see the impact of changes. But that only gets you so far - how do you know which trends are meaningful and which are just noise? To understand why people are doing what they do, you need other forms of research to flesh them out.
One question surveys are a great way of finding out why people are on your site, and whether they've succeeded in achieving their goals for being there. We linked survey answers to analytics for the last Let's Get Real project so we could see how people who were there for different reasons behaved on the site, but you don't need to go that far - any information about why people are on your site is better than none!
5 second tests and lightweight usability tests are both ways to find out how well a design works for its intended audiences. 5 second tests show people an interface for 5 seconds, then ask them what they remember about it, or where they'd click to do a particular task. They're a good way to make sure your text and design are clear. Usability tests take from a few minutes to an hour, and are usually done in person. One of my favourite lightweight tests involves grabbing a sketch, an iPad or laptop and asking people in a café or other space if they'd help by testing a site for a few minutes. You can gather lots of feedback really quickly, and report back with a prioritised list of fixes by the end of the day.
Semi-structured interviews use the same set of questions each time to ensure some consistency between interviews, but they're flexible enough to let you delve into detail and follow any interesting diversions that arise during the conversation. Interviews and observations can be even more informative if they're done in the space where the activities you're interested in take place. 'Contextual inquiry' goes a step further by including observations of the tasks you're interested in being performed. If you can 'apprentice' yourself to someone, it's a great way to have them explain to you why things are done the way they are. However, it's obviously a lot more difficult to find someone willing and able to let you observe them in this way, it's not appropriate for every task or research question, and the data that results can be so rich and dense with information that it takes a long time to review and analyse.
And one final titbit of wisdom from a musical - always look on the bright side of life! Any knowledge is better than none, so if you manage to get any audience research or usability testing done then you're already better off than you were before.