Kindergarten teachers typically introduce addition to their students near the end of the year. You can prepare your child for this introduction with some simple activities. It's important to remember that the language you use with your child is important.
To begin you will need simple counters: beans, legos, macaroni, snacks, etc. Have the child place the counters into two small groups of 2-5 objects. Ask the child to count the number in each group, then put the groups together to count them all. Once the counting is complete, be sure to ask, "How many were there in all when you brought the two groups together?" The idea here is to simpify the concept of addition being the bringing together of multiple groups.
After the child practices this type of counting (one group, then another, then all together) it is time to introduce the addition and equal signs. I like to use a dry erase board but paper and pencil works just fine. Place the two groups near each other just like the prior counting. Write a plus sign between the groups and an equal sign after the groups. Make sure the child knows that the plus sign tells us to bring the two groups together. Just like before have him count each group then the total. This time, have him write the total number after the equal sign. After the activity is repeated a few times, ask "What does the plus sign tell us?". The build-up of this exercise is intended to gradually and explicitly explain what the symbols mean.
As a kindergarten teacher, I notice many times that children can add numbers and count well but they misuse the plus and equal signs, assuming they can come in any order. Once the child has practiced using the polus and equal signs, try writing the signs somewhere else on the paper, away from the counters. Ask if this makes sense. (Typically, children will realize that this looks unconventional and say no). Compare the addition problem to a sentence from a story book and describe that the numbers can go across like a sentence, or straight up and down like a grocery/Christmas list.
Once the child has had experience adding two groups of objects, begin to have them write the numbers below the objects, making a true number sentence. After this practice the child should be able to solve number problems fairly well. Remember to reinforce the purpose of the plus and equal signs.
Have fun adding!