Logistic regression is a form of predictive modeling where the variable you're predicting has a binary or yes/no answer.
Variable selection can be exploratory or confirmatory. In confirmatory analysis, pre-planned models are created and compared for fit and provide relative significance to the model for each value. The best model is the one which balances prosody with explanatory power.
In an exploratory analysis, starting from either a model containing all variables or no variables, perform a stepwise model creation to ensure you have good model fit and that the compared models are nested and therefore valid for comparison to one another. Methodology for selecting which variable to include or exclude is often implicit, but this is likely based on the significance (p-value) of each variable, and the correlation between that variable and the outcome variable.