1.The varsity team will play as soon as the junior varsity is finished.

2.Thirty laps is the most that I have ever swum.
3.My sister was going to take me to dinner, but her car wouldn't start.

Identify each independent clause in each sentence and each subordinate clause. Then tell if the sentence is simple, compound, complex, or compound-complex

1.simple
2.simple
3.My sister was going to take me dinner=independent clause
her car wouldn't start=independent clause
compound sentence

Still not real sure after looking at the web-sites.

You are right about #3.

For #1 --
The varsity team will play = ind cl
as soon as the junior varsity is finished = dep cl

For #2 --
Thirty laps is the most = ind cl
that I have ever swum = dep cl

Note the existence of an introductory (signal) word/phrase at the beginning of both dependent clauses: "as soon as" and "that."
http://grammar.ccc.commnet.edu/grammar/clauses.htm#dependent

1. The varsity team will play as soon as the junior varsity is finished.

Independent clause: The varsity team will play
Subordinate clause: as soon as the junior varsity is finished
Sentence type: Complex sentence

2. Thirty laps is the most that I have ever swum.
Independent clause: Thirty laps is the most
Subordinate clause: that I have ever swum
Sentence type: Complex sentence

3. My sister was going to take me to dinner, but her car wouldn't start.
Independent clause 1: My sister was going to take me to dinner
Independent clause 2: her car wouldn't start
Sentence type: Compound sentence

In sentence 1, the independent clause is "The varsity team will play," and there is no subordinate clause. This sentence is simple.

In sentence 2, the independent clause is "Thirty laps is the most that I have ever swum," and there is no subordinate clause. This sentence is also simple.

In sentence 3, there are two independent clauses:
- "My sister was going to take me to dinner"
- "her car wouldn't start"

There are no subordinate clauses in this sentence. Since there are two independent clauses joined by the coordinating conjunction "but," this sentence is considered a compound sentence.