Is your dependent variable a category (described with percentages instead of mean/SD) or a continuous variable (uses range/mean/SD instead of percentages)?
Category. Continuous.
Use chi-square (if your independent variable is a continuous variable, you will likely need to convert it into a category variable with a smaller number of ordered sublevels).
Is your independent variable a category or a continuous variable?
Category. Continuous.
Use correlation (Pearson r).
How many category levels?
Two (e.g., gender). More than two (e.g., religions).