Check that the degree of the numerator is exactly one more than the degree of the denominator
If not, there is no oblique asymptote
Divide the numerator by the denominator using polynomial long division or synthetic division
Write the function as quotient plus remainder over denominator
The quotient is the oblique asymptote
If the quotient is linear, use that line as the oblique asymptote
If the quotient is not linear, there is no oblique asymptote
Verify by taking the limit of the difference between the function and the quotient as x approaches infinity or negative infinity
The difference should approach 0