This is a difficult question to answer due to its vagueness.  In terms of whether cause-and-effect or merely association can be concluded is based on the study design and the degree to which randomness entered the observational study or experiment.

Do you have a more specific question, such as, how to interpret a specific parameter estimate, how to check conditions, etc.?

Depends on how the data were collected or how the system was simulated. It also depends on how the regression analysis was performed. Was the regression based on a well known model, or based on "best fit?" What type of regression was used? There are a large number of choices here. It includes transformations of the data (log, square root, etc...). As a set of random words that could be used to describe a regression model: polynomial, ridge, segmented, repeated measures, logit, stepwise, and the list goes on. Were any of the assumptions of the model tested, or can you rely on the authors to have considered the consequences of the model failing those assumptions. The real default is that the model fails all assumptions, so the real questions are "does that matter" and "was anything done to reduce the consequence of such failure?"

Are you asking about results that you have generated or interpreting results others have generated? Are you asking what conclusions you can draw about data that you have, or about figuring out if the conclusions someone else made about their data are appropriate or relevant to your work?

It is really very easy to draw inappropriate conclusions from regression analysis. You have asked a harder question, so we need more details.

Regression Analysis is used in the broader sense;  however, primarily it is based on quantifying the changes in the dependent variable(regressed variable) due to the changes in the independent variable by using the data on the dependent variables. This is because all the regression models whether linear or non-linear, simple or multiples relate the dependent variable with the independent variables.

Thank you Timothy A Ebert and  Mohammad Munir for the descriptive answers.