Step 1: What the tests probe.
The key quantity is the number of hydrogen atoms sitting on nitrogen. Primary amines keep two N-H bonds, secondary amines keep one, and tertiary amines keep none. Any reagent that needs an N-H will therefore behave differently for the three classes.
Step 2: Hinsberg reagent as a separation.
Treat the amine with benzenesulphonyl chloride. A primary amine makes a monosubstituted sulphonamide whose remaining N-H is acidic, so alkali pulls it into solution. A secondary amine makes a disubstituted sulphonamide with no acidic proton and it settles out as a solid even in alkali. A tertiary amine, lacking N-H, is left unchanged and floats as untouched amine. Watching solubility in KOH thus separates all three in one experiment.
Step 3: Confirming primary amines separately.
A cross-check is the isocyanide test. Heating with trichloromethane and alcoholic potash converts a primary amine into a foul smelling carbylamine, R-NC. No other class gives this odour, so a positive smell pins down a primary amine.
Step 4: Assigning each structure.
Count the carbon arms on nitrogen. C6H5NHCH3 has two arms (ring plus methyl) and one N-H, so secondary. CH3(CH2)2NH2 has a single propyl arm with two N-H, so primary. (CH3CH2)2NCH3 has three arms and no N-H, so tertiary.