So right now they don't have equal civil rights to other Israelis? I've heard about their poor treatment but don't the extent of it.
There's a distinction between Israeli Arabs and "Palestinians," in that the term "Palestinian" is most often used for an ethnically Palestinian person who does not have Israeli citizenship, whereas an Israeli Arab may or may not be ethnically Palestinian but is an Arab and does have Israeli citizenship. The vast majority of Palestinians do not have Israeli citizenship and thus have very limited rights (rights, in the practical legal sense come from a State).
The Palestinians are under military occupation and have been for generations. Israeli Arabs are ... effectively discriminated against, rather severely...
While many will try to play games about the extent of this discrimination, it exists, even within the confines of the law. Israel has it's problems with racism, just like many other countries and it's not limited to Israeli Arabs but plenty of Israeli Jews who aren't Ashkenazi as well (racism is rarely limited to one group)... but that's another topic that's rather complex.
Regarding the Palestinians, the argument has been that the West Bank and Gaza Strip are effectively "territories" that are either (a) stateless, or (b) in the beginnings of forming a national entity. So, Israel occupies these areas as protectors of both the people in them, as well as the State of Israel itself until such time as a negotiated peace settlement can be established that "guarantees" the Israelis certain preconditions that have been non-negotiable for decades. Thus, in effect, "keeping the peace" through perpetual occupation.
However, over the decades, settlements and continued creeping annexations have effectively turned what would have been a Palestinian State (~1967 borders) into a piece of swiss cheese. There is no contiguous Palestine, or even a contiguous West Bank -- and whenever you hear someone tell you about a peace deal that the Palestinians turned down, keep in mind, they turned down the creation of a Palestinian de-militarized "state" which, like it is today, would have consisted of 4-6 Apartheid-like Bantustans (see: South African Apartheid).
It's a very very unfortunate circumstance for the people living there.
But their conditions are.. abysmal; particularly those living in Gaza.