Skip counting is the most common way to introduce children this young to the concept of multiplication (e.g. 2,4,6,8 or 5,10,15,20).  The website below gives you lots of ideas, including manipulatives (objects) the child can use, songs, actions, etc.  Toward the bottom of the page, (Skip Counting Leads to Understanding Multiplication) it shows how to extend skip counting into multiplication by grouping objects on pieces of colored paper and counting the number of groups - one of the clearest ways to illustrate multiplication:

http://www.squidoo.com/counting

For fast learners, I have also used rectangle multiplication from the National Library of Virtual Manipulatives.  It shows the concept in grid form.  You can translate that to physical manipulatives by having the child duplicate the grid with objects, then having him or her wrap string or yarn around groups (e.g. five groups of five = 25):

http://nlvm.usu.edu/en/nav/frames_asid_192_g_1_t_1.html?from=category_g_1_t_1.html

It's good to introduce a child to the grid format because by grade 3, standardized math test questions often require interpeting shaded boxes in a grid.

I forgot to mention that Mr. Donn at pppst.com has links to many Powerpoint presentations on multiplication as well as online math games for kids.  Of those listed, Multiplication Stories written by Students would be great as an introduction or review and tie into learning activities:

http://math.pppst.com/multiplication.html

I use a game called "Circles and Stars".  You need a set of dice and a piece of paper and a pencil.  The child rolls the dice.  (say its 2).  Then he draws 2 big circles on the paper.  He rolls the dice again. (say its 3).  The puts 3 stars in each circle.  then he writes out 2 sets of 3 stars is 6.  He can count the stars to get to the 6.  Play over and over again.  After a few days start writing the equation (3X2=6).  

I used to use this with my kids in the classroom all the time and they LOVED it.  They became so familiar with it that if they were doing a worksheet and an equation came up that they forgot the answer - they would draw the circles and stars!

Have Fun!

Please see the 5th section of the linked article (of tips for helping kids do better in schools). Section is called Math and Counting. A very simple method using tile floors.