This is a good question. Here is a break down of the sentence.
The subject of the sentence is "ring." The word "class" describes what kind of ring; in other words, it is an adjective. The verb is "lay." It is called an intransitive verb, because it does not take a direct object. The word, "there" is an adverb.
The sentence can be tricky, because of word order. Keep in mind that there is some flexibility in word order in English. If we were to change the sentence around, then the sentence would be much easier in terms of grammar. Here is what I am talking about:
"My class ring lay on the ground there."
The subject and verb is very clear at this point. When in doubt, rearrange the sentence.