Listing in Japanese

I heard one of my friends say 美味しかったし楽しい, which means it was delicious and fun to. I know katta makes something past tense and I know the words oishi and tanoshi, but I have never seen shi used in that way, is shi another way to say and? How do you say "and" in japanese? Do they use "and" much? because I never hear it, and I don't know how to list things in japanese do I do this: 1,2, shi 3.

That is a very colloquial way to say things. What the textbooks tell you would be:
-oishikute, tanoshikatta.
To string up adjectives, you take the te-form, and the past tense should come at the end.

However, lately people say ...shi, often elongated like "shiiii," and continue on with the sentence liberally.

In this case, another construction comes to mind. If you want to list a few sentences or clauses, you can connect them with "...shi."

So the speaker might have wanted to use this construction, as the subject of these two adjectives, delicious and fun, cannot quite be the same (the meal was delicious, and the get together was fun), that may be the reason why that person nearly made two separate sentences without mentioning the subjects.

That person could have said,
Shokuji wa oishikattashi, tomodachi to aete tanoshikatta.
(The meal was delicious, and meeting up with friends was fun.)

The expression you mentioned is simple and informal. We never say that in formal situations. However, the expression is often used in daily conversation. The parson should tell subjects of the verbs, 美味しい and 楽しい。I would say as follows.
食事は美味しかったし、会話は楽しかった。
Meals were delicious and conversations were fun.

In this case, each sentence can be described in the past tense.