You can offer (just about) anything to her--water, fruit, milk, flowers, rice, a piece of cloth, etc. I usually go with fruit and water, myself.
You can also chant a basic mantra for her, like "Om Shri Kalikayai (or Kalyai, whichever you prefer) namah." This is usually translated as "I bow to the Goddess Kali," or "Salutations to the respected Kali," or something along those lines. You can do this as many times as you like, but the traditional number is 108, or certain multiples of 108, like 3, 9, 27, and 54. The number is less important than the devotion behind it, though.
For devotional songs, you can always search Kali bhajans or something on YouTube. It's (usually) possible to find Roman transliterations of them somewhere online so you can sing along without having to guess blindly at the words and even English translations sometimes. (Beware searching for English translations of x bhajan, though. It seems most of the people who post things like that on websites and blogs don't know the difference between Roman transliteration and actual English translations. I want to write them all letters that tell them to stop getting my hopes up because converting Sanskrit/Devanagari/whatever to the Roman alphabet does not equal an English translation!)
There's more, I know, but it's 3:00 am here, and I should've gone to bed hours ago.
Hopefully, some of the more knowledgeable folks will come along and help you soon.
Kali Maa is not the main form of Devi that I worship, but I do worship her at times, and she's been nothing but kind to me and my ignorant self. So I feel sure she'll appreciate anything you choose to do for her.
(Edited to include one of my favorite images of Mother Kali.)