What are the steps to complete the table using the given function?

You put the value for f(x) in each case, and calculate for x, 

f(x) = -√(x+2)

When, f(x) = 0

Then, 0 = -√(x+2)
Multiply by -1, and square both sides, 
0 = x+2
x = -1

When, f(x) = -1
-1 = -√(x+2)
Multiply by -1 and square both sides, 
1 = x+2
x = -1

When f(x) = -2
-2 = -√(x+2)
Multiply by -1 and square both sides, 
2 = x+2
x = 0

So, The basic steps would be:
Step 1) Multiply by -1, in order to eliminate the negative sign
Step 2) Squaring on  both sides, 
Step 3) Simplify by bringing similar terms together

Hope this helps!