Step 1: Three forces decide basicity.
In water, the push of alkyl groups, the help from solvation, and the block from crowding all act together.
Step 2: Find the balance point.
For methyl amines a secondary amine gets a good push from two groups while still being well wrapped by water.
Step 3: Read the order.
The order is secondary above primary above tertiary. So dimethylamine, $(\text{CH}_3)_2\text{NH}$, is the strongest base here.
\[ \boxed{(\text{CH}_3)_2\text{NH}} \]