Example of complex sentence: She asked her husband to make sure to paint the roof and to make sure to not leave any spots in the eaves unpainted.
A complex sentence is a sentence containing a subordinate clause or clauses. This means that there is an independent clause (which means it can stand as a sentence by itself) and a dependent clause (which means a clause that cannot stand as a sentence by itself because it will not make sentence). In the example above, the independent clause is 'She asked her husband to make sure to paint the roof' and the rest is the dependent clause.
Compound sentence: She used to love going up to the roof and sitting with her feet dangling by the eaves because the stars could clearly be seen from there.
A compound sentence is a sentence with more than one subject and predicate. In this example, there are 2 subjects: she and stars. There are also 2 corresponding predicates.