The most common split in methodologies is between qualitative and quantitative methodologies.
A quantitative methodology takes a path a qualitative methodology tries to avoid. Because of this there are much more individual qualitative methodologies than quantitative methodologies.
The path defining a quantitative methodology is the following:

1. the researcher starts by being a realist and an experimentalist;
2. the researcher takes a normative approach;
3. inside his newly defined model the researcher choses some main notions;
4. he posits in the form of a hypothesis (1) a correlation between a subgroup of main notions (called independent variables) and another subgroup of main notions (called dependent variables), or (2) that some notions are more important than others, or (3) any other relation;
5. more often than not the model has a mathematical expression (although prerequisite assumptions are seldom checked); thus, as an example, the presumed correlation between the independent and dependent variables can be computed;
6. the result of the computations (usually numbers) are interpreted back in terms of the initial main notions.

The quantitative methodolology can very well be used as an example in writing a dissertation with a piece of software as its central part. Then you have to follow the next steps:

1. take a snapshot of the situation of your object of study (company or the like) before the introduction of your software
2. find main variables in the snapshot
3. formulate your hypothesis: the independant variable is the introduction of your software and dependant variables are other main variables
4. if the snapshot includes also a company problem which could be alleviated by changing the software environment, harvest all requirements for the software; if not, give up: you might have formulated wrongly the main variables
5. create the software on the basis of the requirements
6. test the software against the requirements
7. introduce the software in your object of study (e.g., company)
8. take a snapshot of the situation of your object of study after the introduction of your software had the time to produce some change in the dependant variables
9. find out if the changes in the dependant variables are significant; if there is no significant correlation between the independant and dependant variables, then reject your hypothesis

Ethnographic Research is a qualitative methodology used to study a culture strange to the researcher. This methodology always focusses on what individuals from a population are actually doing, not what they pretend they are doing nor what they ought to be doing. The researcher is supposed to use empathy to try to understand the culture in focus without going native. This methodology subscribes more to an aprioric position than most other methodologies. While a few ethnographic researchers sympathise with an experimentalist stance, most such research is deeply steeped in the naturalist position. In the latter case the researcher has the function of a sounding board for the culture in focus.
Ethnographic research is the exploratory methodology par excellence. If your hypothesis is not closed and clearly circumscibed by previous reserch, it is quite a good idea to consider this methodology. Of course, you will have then to put up with the appearance of messiness in your research, although you might very well know what you are doing. The rewarding side of such a research are surprising insights and results. The most difficult part in ethnographic research is keeping out any real mess from the application of this methodology.
Your diary about the population under study is not only a legitimate but might be even your main data source. Of course, it is quite useful in such circumstances to be fluent in text analysis.
This methodology can be used successfully in disserations asking about how or why questions about organisational learning, organisational change, information processes (e.g., why some specific software projects fail?) or alternative ways of working (e.g., teleworking). In all these cases the culture in focus is shared by some employees of some organisation. What you do study when using this methodology is always that specific culture.
You might want to have a look at (Myers, 1999) for a good start in this kind of research.

Observational Research differs from ethnographic research mainly by the fact that the latter declares that its object of study is some culture while the former does not make such an overall declaration. In this sense the latter methodolology is a special case of the former. I have to qualify this generalisation: observational research is usually not so open in scope as ethnographic research. It is quite customary in the case of observational research to have quite a clearly circumscribed object of study, much less hazy than "culture".
As in the case of ethnographic research observational research is mostly apriorist and naturalist.
Observational research is essentially a social science methodology. In all cases its object of study continues to be beings like in the special case of ethnographic research.
A question which suggests the appropriateness of this methodology might be e.g. of the form how does A influence B?, where the population is exposed to A and B is an expected (usually psychological) reaction of the population to A.
This methodology is inappropriate for so-called technical dissertations.

Participatory Research can have its object of inquiry as heterogenic as observational research. Again, the object of inquiry is of the social science type. Again, this methodology is apriorist. Naturalism however, is at the core of this methodology: the researcher participates actively to the events under scrutiny happening to the given population; he is clear part of the equation. We could say that the researcher is at the same time subject of the research and source of information. What the researcher has to take care about is not to play also the role of catalyst; in such a case he would study mainly himself, which is not the purpose of any usual research.

The previous three qualitative methodologies could be considered simple (that does not mean easy); the following three qualitative methodologies would then be composite. All 3 following methodologies stem from social sciences.

I consider Case Study to be a composite methodology because of the central rôle played by the triangulation of methodology strategies employed in such a research. The triangulation is essential in this methodology because of the fuzzy boundary of the area of enquiry with its environment and the acknowledgement of the influences of this environment proper in the research. This implies a plethora of variables, much more than the data which the researcher could possibly gather. In order to refute or accept the hypothesis with any confidence one has then to corroborate the data in more than one way (that is, triangulate among plural methodology strategies).
The best book to my knowledge dedicated to this methodology has been written by Robert Yin.

Grounded Theory is a methodology which stands out by the inductive process at its core. Instead of positing a theory (i.e., a relationship among variables) and then trying to validate or invalidate that theory, the present methodology starts with just an area of investigation, remaining open to any theory which might emerge. It is impossible to adopt successfully this methodology, if you do not have what is termed theoretical sensitivity. Theoretical sensitivity refers to the researcher's insight with regard to the gathered data. If you think you can analyse data only in a pedestrian, blunt way, Grounded Theory is not for you. It is customary to call the data analysis leading to theory "coding". There are 3 kinds of coding:

• open coding,
• axial coding,
• selective coding.

Action Research has been first devised by Kurt Lewin. This methodology might take quite some time to be applied fully, in fact it might be argued that it is open-ended. This methodology is iterative and essentially political. If you want to change a state of affairs, you might want to consider this methodology. The iterations take place in cycles of observation -> action -> assessment -> observation ....etc.. You observe first the situation and plan some action, then you act and then you assess the results of your action. This again leads to the second cycle of observation of the state of affairs and the plan of the next action and so on. This methodology is both practical and theoretical. The theory is elaborated sequentially in the assessment phase when this is contrasted with the previous observation phase.