There are many different ways to go about researching. Remember research is done for a purpose – to find something out or seek better understanding. It depends on what you’re trying to do when it comes to find the best way to do it. Think of it like a toolbox – you need the right tool for the job. It’s about seeking the best evidence you can for your research question / application. Try not to think about any one single approach being the only way and try not to think in terms of ‘right and wrong’ ways, just the best for the research question at hand.
The normal overview of research methods firstly divides things into quantitative and qualitative – although many examples of research use a combination of the two, called mixed methods.
Basically, quantitative methods focus on quantities and measures, such as numbers and statistics. Quantitative research can tend to focus on the control and precision of elements involved, as within experiments, and can be good at being replicable (repeated elsewhere).
The notion of being a hard, provable ‘fact’ through data is sometimes referred to as ’empirical’ or ‘positivism’ or ‘realism’.
Common research tools within the quantitative approach include statistical analysis.
Qualitative methods can tend to focus more on human perspectives and ‘insider’ understanding and context, but there is sometimes a challenge in achieving ‘replicability’ on the basis of each specific situation or context being unique. This means it may be hard to justify any ‘generalisable’ claims. Qualitative approaches can be good when you are asking ‘why’ things happen.
The notion that everything is really a matter of perception and individual meaning is sometimes called social constructionism or relativism.
Common research tools for the qualitative approach include focus groups and interviews.
The pros and cons of each approach show why mixed methods can produce a better outcome, where appropriate.
For a little more light reading (there is a lot of information out there!) you could consider A Gentle Guide to Research Methods by Gordon Rugg and Marian Petre, published by OUP.