To change the climate of the entire earth requires a change in the balance of radiation.
Energy in = energy out - stable climate
Energy in less than energy out - earth gets cooler (ice ages)
Energy in more than energy out - earth gets warmer (interglacials)
Temperature is one way of measuring energy. The same object measured at a higher temperature has more energy than that object when it's cooler.
When as much energy goes out of the earth as comes into the earth, there won't be a global temperature change. There will continue to be changes in climate in different parts of earth but it will balance out over the whole earth.
The temperature of the whole earth is rising and has been more or less doing so since about the time the industrial revolution took off. This rise in temperature can in essence be only from one of two causes. Either there is more energy coming in from the sun or there is less energy going back out to space from the earth. (If the earth was cooling it would be the reverse.)
The reason the earth is warming is that the earth is holding in more energy than is going out into space. Since the middle of the 20th century, measurements of the sun's energy and the earth's current orbit and the way it is aligned to the sun show that the earth has not been receiving more energy from the sun. (Before this time, some of the extra heat can be attributed to there being more energy coming in from the sun as well as the extra CO2.)
The greenhouse effect describes how earth retains heat to support life on earth. The recent rise in temperature is mainly caused by the large rise in one of the greenhouse gases, CO2, which means less energy is being radiated out, which means the earth is getting warmer. As a result of this initial warming, there are other effects that all add to the change - water vapour, which is another greenhouse gas, increases and lets even less energy escape, ice reduces and means less energy is reflected out to space, and so on.
Eventually, the energy state will re-balance. The temperature will stabilise at a new higher level and the amount of energy coming in will again equal the amount of energy going out.
An analogy of the adjustment to the change in energy balance is - if you turn on a tap over the sink and allow the water to drain out the plughole. If you partly plug up the drain then water will start to rise in the sink. There will be more water coming in from the tap than going down the drain. This is the same effect as adding more CO2 blocks some of the heat from leaving the earth, and the energy increases and temperature rises. For a while the water will continue to rise in the sink (similar to the temperature going up) until it reaches a point where the water coming out of the tap equals the water going down the drain. The pressure of the water in the sink will cause more water to go down the drain and equalise with the water coming out of the tap. The water level will be higher when it equalises, just like the temperature will be higher when the earth's energy balance gets to a new equilibrium.
The above description is a very simplistic description of the situation. Much more detail is available from reputable sources closer to the science itself. Check the links here for a more detailed and scientific explanation and other related information.