It depends on what about the furnace unit is making the noise.
Typically it is the fan motor, or associated moving parts.
Sometimes it is the housing vibrating from the spinning of the blower fan. It may be the plenum or metal (or other) box that the air blows through to get to the ductwork.
Lets look at all reasons it can make noise and eliminate things
First, the fan. If the furnace/ac kicks on and there is a rattling or grinding or whining or other noise that accelerates as the fan picksup speed, the bearings in the fan blades or motor are going bad. This is not good/expensive to fix maybe.
IF the noise is worse when the fan is at full speed and stays constant while the unit is blowing air it could be that the belt is loose or if no belt the linkage from motor to blower fan is loose or worn out. This may be fixable with a little tinkering but not for someone not mechanically inclined. The mounting for the motor or fan blower may be loose, try to tighten the screws or bolts that hold them down.
If the noise starts slowly after the fan is at full speed it could be that there is resistance in the plenum or ductwork/air ducts/vents. This usually isn't that noisy, but it can be bad.
You should go throughout the house in each room and make sure that the ducts are clear and vents are all open to the full. Usually there are fins that direct the flow to a certain direction these should be open wide, also behind them may be a flow restrictor fins. These are used typically with a lever that opens or close the flow off completely to 'zone control' the room. These should be open wide as can be too for the testing. Should be so the air ducts and vents in each room are open wide and blowing air full when the unit is operating. Be thorough as you search for vents in all rooms, you may miss a vent or two in odd rooms, behind furniture or in larger rooms. If any air vents are open wide and don't blow air with good force(should be similar from vent to vent and from room to room, decreasing slightly the farther from the furnace unit you get) then the ducts(tubes) are blocked somehow. if they are in the attic, they may have been crushed by the cable guy or the christmas ornaments box you shoved up there. or maybe you have squirrels building nests within them or something ( similar in the basement depending where the ductwork runs.)
If they are smashed, reshape as best you can and see if that gets the air going again. (careful not to tear them open or cause leaks in the duct itself) If too much air is restricted from coming through the ducts it can make the unit more noisy. If the ducts leak into the attic or basement you lose heat/cool into that space instead of the room and could cause water damage from condensation. Seal leaks with duct tape or replace the duct.
Same goes for the return air intake(s) usually there is one at the furnace unit on the door to the unit or an adjacent wall. The filter usually goes there. the filter should be clean and fit properly for the opening so all air goes through it not around the edges. Other return air ducts can be placed throughout the house in larger homes so check that the same as the air ducts and clear any blockages. Sometime when the unit is installed, the unit is too powerful for the size of ductwork existing and this can backpressure the unit causing excessive noise and resultant loss of efficiency of the entire unit. It is working too hard to force air through it. This is hard to calculate, a bigger plenum and more ductwork is required.
Other major noise may be the plenum, duct work, vents or surrounding wallboard or the floor where the unit sits may be loose and making vibration noise that can be dampened by securing it properly/better... if it is rattling or humming it may be the plenum or duct work. Tap on the plenum and ducts to see how loose they are and if so, try to screw, rivit or tape the parts that are noisey so they can't flex so much. This may dampen the sound a bit.
Make sure that the floor under the unit is solid and doesn't have any weakness at all.
Sometimes there is water damage from condensation or poorly braced for the weight of the unit or other reasons that weakens the joists or flooring and that can really make it noisy but not be obvious. unfortunately, this may be an expensive or extensive job to fix but maybe worth the trouble if the floor is damaged enough to break under the unit.
This should eliminate most of the noise of the unit that can be fixed. Sometimes you just have a noisy unit. In that case, there are other things to do to help quiet the environment of your living space.
If the furnace is in a wall that adjoins the bedroom or living areas, you might try to place larger pieces of furniture infront of the area where it is. Like putting your big dresser on that wall right where the furnace is located. Maybe hang a tapestry on that wall as well will help quiet it some.
Move the bed or your sitting chair to the other side of the room from the furnace.
Another more extensive fix can be to double up the drywall board around where the furnace is to quiet it down. this seems radical, but it will reduce a noisey unit significantly if done properly. (last resort stuff)
In short, Eliminate any vibration noise, air flow restriction noise, or structural weakening, use sound barriers in the rooms or consider replacing the furnace altogether.
An existing furnace that is over 5 years old (the pros say) is inefficient and can cost up to 50% more in energy cost than a new unit.
A new unit can be much quieter, more efficient and sometimes you can move it to another area that is less annoying noise-wise.
Hope this helps!
Good luck!