Water leakage is an ugly sight, it damages the walls, causes all sorts of mold to grow and weakens the structures. How though do you get rid of it?
For the most part, water leaks will first have to be plugged. Find the source of the water seepage and plug it. Excessive water around the soil of the house is not in any way good for you. It will damage the walls, cause foundation weakness and will lead to all sorts of excessive bills and repairs. If the water leakage is in one spot and only a wall is damaged, it can be cleared up without much effort.
Where is the water coming from?
A wet spot in the basement wall or any wall of the house does not simply appear from a cup of water. It takes a serious amount of liquid to seep through treated walls and a good amount of time before it is apparent. So water can be from anywhere, a dripping drain pipe or a rainwater gutter that is pouring water to the base of the house.
How bad is the damage?
Find a contractor to come and have a look at the damage done. If the damage is manageable and simply letting the walls dry off is sufficient, good for you. If not, sections of the walls may have to be replaced.
How to cover it up?
The most obvious way will seem to be a good layer of paint over the wall. It may work, but you might as well get a few layers of shellac based primers and other treatments done so that it stays the way you want it to.
Will paint be enough?
Yes, if the walls do not need any other work to be done on it, paint will be sufficient. It will do you good to check with a professional before you decide to paint the walls though, just to be sure.
When paint is not enough
Keep in mind that while paint protects from wetness, it is mostly just a cosmetic procedure. So do not run to a wet wall with a can of paint thinking it will take care of the wetness. It will not, and in fact, by covering a wet spot with paint and doing nothing else will only make it worse. It is akin to pushing garbage under the bed, the room will look neat, but it will still be dirty on the inside.