The inverse Laplace Transform can be calculated in a few ways. If the function whose inverse Laplace Transform you are trying to calculate is in the table, you are done. Otherwise we will use partial fraction expansion (PFE); it is also called partial fraction decomposition. If you have never used partial fraction expansions you may wish to read a background article, but you can probably continue without it.
There is also a way to directly calculate the inverse Laplace Transform by integration (so called "Direct Calculation"). The technique is described, but no examples are given. This takes advanced calculus and we will not use direct calculation.
Finally, examples are given the use MATLAB. MATLAB has powerful techniques for partial fraction expansion.