Depends on how old it is. If it's ten years or less old, I would have it checked by a plumbing company or a plumber someone might refer. Past ten years? Replace it. Easier and good for years to come.
My electric water heater had been turned off for 6 weeks. When I turned it on last night, the water was much too hot; and a puddle of rusty, sticky water is at the top of the heater around the pressure-relief valve. Are these fixable problems?
The reason the water is getting too hot is probably due to a sediment build up on the heating element at the bottom. Basically, the sediment gets so thick that it insulates the thermostat and the thermostat thinks the water isn't hot enough so it ensures that the elements are on and heating water most of the time.
You can change the thermostat and element yourself fairly easily, but you will need to make sure that the power to the heater is totally off (don't take a chance here) and you will also need to drain the heater which can take some time.
All I would say is that you need to be careful if you are not too clear on how these things work. The last thing we want is for you to have an accident or cause a fire.
This website http://www.waterheaterleakinginfo.com/ gives some good information so you might want to take a look there to determine your problem and see if it is fixable.
I would certainly looking at fixing before buying new, although if the heater is very old you have to weigh up the cost of repair against how long you can expect it to last.
I've included a video about fixing a leak around the pressure-relief valve of a water heater, I hope you will find useful.