Even motors that "say" they have a 240V connection may actually NOT have that because they were rewound sometime in the past. The wires may not be brought out, and nobody bothered to change the motor plate.
IF it has 240V capability, it will normally have at least 6 wires. There will be two separate pairs of wires which are for the "run" windings. These go in series for 240V, and parallel for 120V. The question is "polarity", i.e. how to get the two connected so they work together instead of opposing each other.
The remaining two wires are for the "start" winding. They will connect across one of the run windings. The "polarity" of the start winding will set the direction of rotation.
Sometimes there are two more wires for a motor protection thermal cutoff.
If the motor wires are connected now, and there are 6, it is just a matter of identifying the run windings and connecting one of them in series with the other two. If not, then you must identify the run windings and their polarity.
The pairs of wires that have the same resistance are the run windings. The start winding will normally be different, either higher resistance, or it may measure "open" if there is a capacitor for starting.
If the run windings are connected the wrong way, the motor will draw a lot of current. Reverse one pair in that case.