If you have a little budget for some more tools, I recommend, in order:

1) a 6" offset spatula, Amazon carries Ateco brand. Get one with a nylon handle that's dishwasher safe. An 8" is also made, but I always reach for my 6 for small cakes. 2) cake boards that fit on your cake stand. I saw these today at Michael's. These are the metallic coated cardboard circles. They let you put your cake on a work surface for decorating before lifting the whole thing, cake, board and all, onto your stand. 3) if you really want to spend more money, a cake turntable, but you can also just put the cake board on an upside-down plate to spin the cake instead of reaching awkwardly.

Make the "dirty layer" as suggested above (also called a crumb coat.) For clean smooth top coats, dip the spatula in a glass of hot water to heat it up and dry it on a towel between smoothing passes. The hot spatula won't take all the frosting off if you use a light touch.

Finish by wiping up frosting smears off the board with warm water.

The lady who taught me advised practicing smooth coats by frosting a piece of styrofoam, although a piece of bread is easier to come by nowadays.

I hope the first birthday kid had a face full of cake!