The techniques applied in the analysis of Bivariate Data depend on the types of data involved in the distribution.
Scatter Plot and Regression Line
When both the variables in a Bivariatle data set are quantitative or numerical type, a scatter plot is used to study the relationship between the two variables. Each pair of variables is considered as an ordered pair and plotted on a graph. The independent variable is measured along the X  axis (Horizontal axis) and the dependent variable is measured along the Vertical Yaxis. From the pattern of the plots, we can analyze the correlation between the two variables.
The above scatter Plot shows the relationship between the average number of hours studied per week and the final score.
A positive correlation can be recognized from the pattern seen. Using the data set a regression line or trend line can be found using various methods. The equation of the regression line is useful in forecasting future behavior.
Numerical Variable and a Categorical Variable
A back to back stem plot or a Histogram is used to display Bivariate data consisting of a numerical variable and a categorical variable with categories.
The following table shows the weights of new born babies in a hypotherical Hospital during the course of a month.

Weights in Kg

Boys 
3.5 
4.3 
5.0 
3.6 
4.9

3.5

3.8 
4.8 
3.6

4.2

Girls 
3.0 
2.8 
3.8 
3.2 
4.1 
3.1 
2.7 
3.3 
3.6 
3.2 
The back to back stem plot is shown above, which can be used for further analysis of finding the median and the quartiles.
When the categorical data consists of more than two categories parallel box plots can be constructed displaying the five point summary of each category.
Example:
The following contingency table shows the ice cream flavor preferences between male and female students
Flavor

Male

Female  Total 
Vanilla 
9

5
 14

Chocolate 
12

20
 32

Strawberry 
12

15
 27

Caramel 
15

12
 27

Banana Split 
12

8
 20 
Total  60
 60
 120 
This contingency table can be used for analyzing the bivariate data using different techniques. The frequencies here can be expressed as percentages and compared. Or this can be used in testing the claim on population behavior using advanced techniques like Hypothesis testing.