It's always written cursive, i.e. the letters are joined together. The letters represent sounds. A letter has the same sound regardless of context. Vowels are divided into long and short ones, and the short ones aren't written. I.e. the word "(he) wrote" is pronounced kataba, with three short a-sounds, is written ktb.
You can write out the short vowels but it's only done in special contexts (like children's books, books for foreign language learners, or the Qur'an). It's easy enough to read if you know the language, but it makes it a little harder to learn.
It's actually not very different. Hebrew works in the same way, except it's not cursive. They share a common ancestor in Phoenician script I think, also used for a Semitic language, for which it works well. The Greek alphabet (and thence ours) was derived the Phoenician script that worked in a similar fashion, by adding vowels.
It is a writing system found in Eurasia. Hit its wikipedia pages, on the right hand side there'll be a little thingie that lists 'parent systems', you can follow it back to Phoenician which also happens to be an ancestor of the Latin alphabet.
You can write out the short vowels but it's only done in special contexts (like children's books, books for foreign language learners, or the Qur'an). It's easy enough to read if you know the language, but it makes it a little harder to learn.