There should be a ground terminal (possibly just a screw or bare or green wire) that you connect the ground wire to.

It's really hard to be sure, you should have noticed how things were connected before you removed the old unit. I'm presuming there are two switches in your previous installation (one for fan and one for light)? In that case one probably feeds the black and the other the white. If that is the case then

the beige (probably just a discolored white) gets connected to both fan white wires. The blue wire goes to either the red or black and the black wire to the other one.

Thanks Ronnatalie

When I disconnected the old unit, I noticed the unit had different wires than this new one so I was confused from the get-go about how to wire the new ones. I went so far as to return to the store I bought it from with pictures of my home's wires so they could tell me what to do but as usual, they were of no help.

I do have two switches on the wall like you said. I will give it a shot!

Thanks for your help!

The most common colors for the wires when there are two devices to switch is:
bare wire - ground
white - neutral (always connected)
black - switched wire if there is only one device
red - switched wire for a second device

Red wire may also be present if there is a 3 way light switch (for two entrances to a room, etc.), or the wiring is for a 240 volt circuit.

Bruce