The idea behind a SMA is simple: you find the average of the most recent five days. So basically you take a certain number of days and find the average over those days. Then every day after that you replace the oldest day with the most recent one. For instance, when finding a 5 day moving average:
On the 5th day the SMA would be (10+11+12+11+13)/5 or 11.4. The next day the SMA would be (11+12+11+13+14)/5 or 12.2. On the 7th day the SMA would be(12+11+13+14+15)/5 or 13.
The EMA is slightly more complicated. It gives preference to the most recent days, but no day is ever entirely taken out of the average (as in the SMA, all days not within the most recent period are discounted) they are just weighted extremely lightly. For instance, in a 10 day EMA, the most recent day would be weighted 18.18% with every preceding day being weighted a little bit less.
What is the difference between these two? Well, to start, since more recent days matter most in EMAs, they are much more sensitive to recent changes. On the other hand, SMAs sometimes lag behind more. The trade off here is that EMAs could sometimes can give false signals whereas a SMA could be more accurate. Another thing to take into account when looking is the length of the average. A shorter/longer average could show the same differences as a EMA/SMA. The longer average will lag more but be more accurate than the average of a shorter period.
What are you going to use a moving average for? To spot trends. Regardless of the volatility of day-to-day trading, moving averages allow you to look at the big picture and see how the stock has been trading over a long period of time. Also, if the stock is trading above the moving average, it can be considered to have an upward trend; if it's trading below, it has a downward trend. Finally, comparing moving averages of different periods can be compared. If the shorter moving average is above the longer moving average, there is an upward trend. If it is below it has a downward trend.
Moving averages by themselves are in no way a determination of whether to buy or sell. It's important to remember that you are only looking at trends in the past. They are not guarenteed to predict the future and can give bad signals sometimes. However, they are a useful tool when you are trying to look at stock trends as one one part of your stock analysis.