I have a light switch and a fan switch next to each other in the same outlet box. You can only use one at a time. For instance, if the light is on and you flip the fan switch, the light goes off and the fan comes on and vice versa. How do I fix this?

Now that's a strange one. Sounds like some one "less than experienced" wire it. Pull switches and tell us what how many and what wires you have in the switch box.

Usually 1 hot wire is pigtailed to another switch. Look at the switches. Does either not say ON and OFF?

It is wired like this. The light switch has wire going to the top screw and a wire going to the bottom screw. The fan has a wire going to the top screw and a wire going to the bottom screw. It.also has a separate wire joining the 2 bottom screws.

Need to know which wires are connected. By two bottom screws do you mean the green ground screws.
How many wires come into the box?

Pull switches out of the box.
Take a picture.

Actually Ma0641 does know what he is talking about, it is you who misunderstood the reasons for his question.

"Look at the switches... " A single pole, single throw toggle switch will have the words On/Off embossed on the handle. Two way, three way and four way switches will not. Understanding the type of switch in the circuit is important.

"Pigtail" is a term used to describe a connection method. In this situation Ma is asking you if you have one source wire to the switch outlet that is connected to two smaller wires. One would go to the bottom of the fan switch and the other would go to the bottom of the light switch.

The top wire on the fan switch would in turn connect to the black on the fan. The top wire on the light switch would in turn connect to the blue for the light package.

Harold also made a reasonable request. Take pictures of both the ceiling outlet box and the switches, after they have been pulled out of their box.

The separate wire you describe may be the bare copper grounding wire that should be connected to the small screws on the lower part of the yoke.

CAUTION, turn off the breaker or remove the fuse prior to removing any parts of the circuit.