To turn a sentence fragment into a full sentence, add a subject or a verb, depending on which component you are missing. In some cases, a sentence fragment is created by composing a phrase that doesn't express a complete thought. If this is the case, complete the thought.
All complete sentences contain, at minimum, a subject and a verb. Sometimes, the verb is referred to as a predicate. Complex sentences contain more than these two components. To be a sentence, the words must also form an "independent clause," or complete thought.
Often, sentence fragments in writing occur when writers compose dependent instead of independent clauses. A dependent clause cannot stand alone because it doesn't address a full and complete thought. For example, "After we went to the store" is a dependent clause. Although this set of words contains a verb, went, and a noun, store, it is not a complete sentence as it doesn't present a full thought. Dependent clauses must be combined with independent clauses to form full sentences. For example, you could say, "We ate the cookies after we went to the store."
Don't just add element after element in an attempt to avoid sentence fragments. Just as a sentence can have too few components and be a sentence fragment, a sentence can have too many and be a run-on.