I hope it's not to late for this post but here is what I find helpful to me:
You will need at least 4 plastic dowel rods and 1 wooden dowel rod). As suggested you can use straws but do not use the ones that have a flexible top. I prefer the plastic dowel rods.
You have a 10 inch and 6 inch cake. The 10 inch cake should sit on a heavy duty board at least 2 inches wider than the cake so in your case you will need a 12 inch heavy duty board. The 6 inch cake sits on a 6 inch board, the exact same size as the cake.
Get a piece of parchment circle paper the size of your top cake (In my example I would get a 6 inch parchment circle). Center this parchment circle over your cake (the 10 inch cake) then mark your bottom cake (the 10 inch cake where the 6 inch cake will sit, mark about 4 places or you can lightly circle the parchment circle). With this parchment circle in place mark the 4 spots where you want your plastic dowel rods to go. To do this just lightly press 4 indentures into the cake.
Now remove the parchment circle and get your plastic rods and slowly press it into the indenture, making sure the rod is in straight, then mark with a edible pin where you will cut off the excess. (note: the plastic dowel rod should be the same height or a little bit smaller than the 10 inch cake). Use this rod that you have just cut to cut the other 3 rods. After you have cut the other rods place all 4 of them in the cake straight and evenly. Then for more support, I normally fill the inside of the plastic rods with frosting. Now you are ready to place the top cake (in this case it is the 6 inch cake) on top of the 10 inch cake. If you are using butter cream frosting leave the 6 inch parchment circle on the cake then place the 6 inch cake on top of the parchment circle. If you are using Fondant you can remove the 6 inch parchment circle before placing the 6 inch cake on top of the 9 inch cake. If you are using Fondant this last step is up to you on whether you leave the parchment circle down or you remove the parchment circle. Now get a long slender dowel rod and measure it from the table to the top of the cake mark this spot. Now cut this dowel rod with a pencil sharpener the height of the top cake (note: this is done for additional support especially if you will be transporting the cake already decorated and ready to go). When this is finished, place this rod in the center of the top cake (you might need a light weight hammer to assist you in driving this rod through the 6 inch and 10 inch cake) . Press the rod all the way down until it reaches the bottom board. Now cover this small hole with fondant or frosting. (If you are using fondant as your finished product be sure and place your topper or a design over the small hole. If you are using Buttercream Frosting as your final coat/product cover this hole with more frosting or a topper. I hope this helps.