For this example we will use dataset from SPSS samples: customer_dbase.sav
Select customer_dbase.sav.
Click on Analyze section from the top menu.
Find General Linear Model section under Analyze. Then click on Univariate… button.
Once you clicked you will see the following menu:

In ANCOVA, you will have a dependent variable, factor variables and covariates.
In this example, we will use one factor variable and covariate.
We selected Houshold income in thousands (income) as dependent variable, Level of education (edcat) as categorical / factor variable and Number of people in household (reside) as covariate / control variable.
In ANCOVA analysis, there is one additional assumption: Homogeneity of regression slopes.
In order to test this assumption, click on the Model button on the right.
Click on build terms or custom model.
Select each of the factor and covariate. Then select both of them on the right than click on the arrow button. This way, you will be able to analyze factor variable, covariate and their interaction term.

Once you are done, click on Continue button. Then click on the OK button in the main menu.

What you need to check in the table of Test of Between-Subjects Effects is the Sig. (p-value) of interaction term which is edcat*reside. If p-value is bigger than 0.05, in other words insignificant, then your model doesn’t violate the assumption of homogeneity of regression slopes. In this example, the assumption is not violated (since the p-value of the interaction term is 0.126 which is bigger than 0.05), so we can continue the analysis.
So, you need to click Analyze -> General Linear Model -> Univariate again.
Now, you need to click Model… button on the menu at the right side. Then select Full factorial and continue.
After that click on the Options… button and select Descriptive Statistics, Estimates of effect size, Homogeneity tests and click on Continue… button.

Now in the main menu click OK… to see the final results.

From the results, we can clearly say that Level of education (edcat) and Number of people in household (reside) have significant impact on Household income in thousands.