There multiple solutions and this is just one of them.

0  = 4+4-4-4.

1  = 44/44.

2  = 4+4-(4!/4).

3  = (4+4+4)/4.

4  = 4!-(4*4)-4.

5  = (4!/4)-(4/4).

6  = (4!/4)+4-4.

7  = (44/4)-4.

8  = 4+4+4-4.

9  = 4+4+4/4.

10 = (44-4)/4.