Conversion of RE to NFA
An epsilon transition (also epsilon move or lambda transition) allows an automaton to change its state spontaneously, i.e. without consuming an input symbol.
You need them for two cases
$1.$ The string or part of the string includes a Kleene star $^*$. E.g. $(10)^*$
$2.$ We have the option to choose between different strings. E.g. $0|1$
Now to make the string $$1^*(00|011^*)^*00$$ much easier, we will split the string in different steps.
Step $1$: Find NFA for $1^*$. We can do this by the following

Step $2$: Find $(00|011)^*$. We will skip $1^*$ to make it ourself easier.

Step $3$: Now we add $1^*$ to the previous NFA. We actually can 'substitute' the DFA in step $1$.

Step $4$: Make sure the string ends with $00$.

If we combine the previous steps, we get the following

You also can always check your answers by a RE to DFA/NFA converter.
Note: The above NFA is made inductivly and can be reduced by removing $\epsilon$ transitions as it is not necessary.