This is a pretty common problem on the older PS2s, but it's not always a laser issue. If your PS2 makes a funny squeeking/grinding noise that results in a disc-read error, then the problem is worn guides on the laser arm and not the acutal laser. I actually just had this problem on my PS2, if the guides aren't too worn down, you can do what I did: Remove the laser arm, carefully heat it with a cigarette lighter until it's warm enough to be a bit plyable, then pull down on the arm so there's just a slight curve to it. When the arm is installed back on the laser lens it will have just a bit of downforce on the laser gear to keep it from slipping.
If the guides are pretty well toast, replacement arms can be purchased for around $10.
If the disc just spins without these funky sounds then yeah, you have the typical laser problem. There are two possible solutions, cleaning/adjusting the height of the laser lens and adjusting the laser voltage. Google "ps2 laser adjustment" and you should find all kinds of info on the repair. Make note of your specific PS2 model, because there will be some differences between the models.