An example is I know a spot needs a 22uF 25v cap but all I have in my kit are 22uF 50v caps. Is it ok to go above the voltage as long as the uF rating is correct?
Yes sir! Not only is it OK, it's better! I've answered this quite a few times here, spreading my newly acquired Le Steve knowledge.
http://www.pcenginefx.com/forums/index.php?topic=7012.msg298464#msg29846416 V is OK/safe. The circuit board generally operates at ~5 Volts DC after the power regulator, so capacitors that are rated 10 V or above are safe. But the bigger they are, the better they are: they last longer, handle "ripple" better and sometimes there is power inverting going on so they need to be of higher voltage in that area of the board. This comes at the expense of size and $$$: a 25 V cap is physically bigger and more expensive than a 16 V cap, etc. Anyhow, I was confused about this as well when I got started, but there ya go. When replacing a capacitor, you simply need to match the capacitance value exactly, but the max breakdown voltage can be equal or higher (and higher/bigger is better/safer).
That voltage rating on a capacitor is the max breakdown voltage, meaning, if the circuit runs at or higher than that, the capacitor is gonna start to overheat, break down, be destroyed, etc.
Most electronics run at 5 Volts DC here, so 16V rated or better caps are fine.
Sometimes, you don't want to be too close to the normal operating voltage though - it's always better to go bigger if you got the space and don't care to have paid more $$$!
E.g. I have a power supply for a 19" LCD TV given to me for servicing that had both 5VDC and 12VDC power outputs. The 12VDC area had 16V caps for regulation which broke down and killed the TV. Given the extra heat in the area, the manufacturer went too cheap and should've used 25V rated caps which would've been a little harder to fit given the PCB design, but possible. So only after 3-4 years of service, this new TV was dead for something as simple as a few capacitors...
Here's a video from the EE I learned a few things from:
He has a dumpster diving TV/monitor repair segment/feature. People throwing away TVs and LCDs that mostly failed due to cheap capacitors in the power supply area for reasons like this which he finds/is given for amazingly cheap repairs most anybody can do! Cheap CapXon brands and rated just a bit too close to operating output voltage is a typical reason for failure.