Step 1: Principle.
In aqueous solution, basicity of amines depends on the electron-releasing (+I) effect of alkyl groups \emph{and} solvation. General order:
\[
\text{secondary}>\text{primary}>\text{tertiary}>\text{ammonia}
\]
because secondary amines have strong +I effect and still good solvation; tertiary amines suffer from steric hindrance and poorer solvation.
Step 2: Apply to given amines.
Least basic $\to$ most basic:
\[
\boxed{ \mathrm{NH_3 \;<\; (C_2H_5)_3N \;<\; C_2H_5NH_2 \;<\; (C_2H_5)_2NH } }
\]
Step 3: Check.
This follows the aqueous-phase basicity trend: 2°>1°>3°>NH$_3$.