What does it mean by "no consecutive zeros"? That means there is at least one 1 between any two zeros. You can express it as something like $01^*1$, if there might be a 0 downstream.
If there are two non-consecutive zeros, you must have a substring like $011^*0$. All other characters must be optional, which should be better expressed separately.
So a possible answer could be,
It reads as a string that starts with zero or more 1's, followed by zero or more strings each of whom starts with one 0 and ends with 1 with possible more 1's in between, followed by two 0's that are separated by one or more 1's, followed by zero or more strings each of whom starts with one 1 and ends with 0 with possible more 1's in between, followed by zero or more 1's. Notice the symmetry, which should help your understanding.
Motivated by oerpli's answer, we can actually remove one part of the expression. For example, we can let the two zeros occur at the end, i.e., no zero is after those two zeros. The shorten expression will be,