Any data analysis starts with an inspection of the descriptive statistics that includes mean, standard deviation, minimum, median, maximum, quartiles and kurtosis as well as skewness. Kurtosis and skewness give hints for normality of the data.
Additionally, a series of graphical displays should be part of descriptive statistics. Time plots, histograms, box plots, dot plots, violin plots or a combination of these are helpful to illustrate characteristics of data.