PCB Antenna Design Calculations
Here you can find some references for microstrip patch antenna design.
Firstly you had to determine target frequency and substrate material. For starter you can use standards like FR-4 substrate material with epsilon_r = 4.3 and 1.6mm thick.
Then you need to calculate patch sizes, you can do it by hand with formulas given in references below or you can use microstrip patch antenna calculator (also given below)
After this easy design steps you can simulate it with simulators (I use CST Studio Suite) to optimize the design parameters
Most appropriate reference for you
Reference 2
Online Calculator
Trailer Video
After some practice with these, you can go forward with array antennas or different shaped patch antennas like circle. Note that, other shapes than rectengular patch antennas need more complex calculations to design.