I removed the old ceiling fan and found 1 black wire by itself and 3 white wires tied together, the old fan had only 2 wires, one black and one white, the white was connected to the group of white wires and the black to the single black wire. I am replacing this ceiling fan with an clarkston 44 inch ceiling fan. This fan comes with a black a blue and a white wires. Should I connect the blue and white to the 3 whites and the black with the black?
There are almost certainly more colored (non-white) wires in the back of the box which are for other hots.
Is the blue wire blue or green? It matters a lot.
A green wire should be attached to the ground wire bundle that may be in the back of the box. Absent that, look and see if the wires enter the box via cable or pipe. If cable and no ground wires, connecting a ground is pointless. If pipe, most likely this conduit is the ground, and the green wire can be attached to the steel box. There may be a tapped hole for a 10-32 screw somewhere in the back of the box. If not and you are crafty you can drill and tap one (any machine screw 6 or larger will do as long as the thread is at least -32).
If the wire is honest-to-gosh blue, then is it light blue? That might be a Euro neutral, but that would be strange. Otherwise it is assuredly one of the hots, you have a separate hot for fan and light, allowing you to control the two of them individually. If you want, you can do some extra wiring to exploit it... Or you can simply connect the blue and black together to the power supply, and fan and light will operate together. Some fans permit local control of light and fan i.e. With 2 pull cords. Those are always fun!
If this fan has a light fixture, the blue wire is probably the hot to the light and the black is the hot to the fan. If this is the case you would connect the black and the blue to the black hot. Separate control of the fan and the light would be by pull chain.
Does the line power to the fan come through a wall switch? The separate hots to the fan and the light would allow separate switching at the wall if you had two switches and two separate cables entering the box, one from each switch, but according to your description you don't have that. And you haven't even said if you have one switch.
I have put in eight ceiling fans and thought it would be acceptable to do without wall switches and just use the pull chains. I was wrong. Wall switches are far preferable to pull chains.