What is multivariate analysis and logistic regression?

In a population based study we compare socio-demographic variables with certain outcomes, e.g. nutritional or micronutrients deficiency. How to apply logistic regression or risk ratio to calculate the risk of having a certain outcome, compared with a socio-demographic variable? What are the requirements for a multivariate analysis test? Is it different from logistic regression? How do we set the regression equation, and how to do the actual test, for multivariate analysis.