As the others have said, (a) it's possible to hook them up, and (b) there's more than one way to do it. It really shouldn't be difficult for you to get those two speakers running, assuming that they still work. Like bikemig said, we can help you work through this.
The reason for the amplifier is that the headphone (or line out) jack on your laptop/iPod puts out enough power to run the tiny speakers that are in headphones, but it doesn't put out enough to run the larger ones in those Sanyos. Hence, you need to boost the power.
From the picture, the input jack on the back of the speaker looks like an RCA jack to me. Some speakers take two bare wire inputs that go into a positive ("+") and a negative ("-") terminal, some speakers use a RCA jack input, and other speakers use some other type of jack. Typically, the ones that don't use bare wires came as part of a larger system that included the receiver or amplifier. For example, a number of "home theaters in a box" and computer speaker sets have jacks on the back of the speakers.
Before getting into which cables to buy to connect to those speakers, I second bikemig's recommendation that you let us know which receiver you have. That will help us know the easiest way to connect things. Also, do you happen to have a computer speaker set? Specifically, one that connect to the speakers using RCA jacks into the speakers? If so, you could try connecting those Sanyos up in place of two of the computer speakers. They might sound pretty quiet because they are larger than the computer speakers, but it might be worth a try just to check if they work.
