The first thing I tried with my kiddos was popsicle sticks. When working with my small group students told me that having so many numbers was confusing. I showed students how to use a popsicle stick to cover the bottom number in the tens place while they multiplied the number in the ones column. Next, students used the stick to cover the bottom number, and answer in the ones column while they multiplied by the tens column. This also helped them line up the answer from the tens column since the popsicle stick served as a place holder. Luckily, about 1/3 of my class had success with this method.
For the rest of my class I had to try another method. We moved on from popsicle sticks to color coded multiplication. I found this idea on pinterest and a few of my kids really seemed to understand better when they used the colored pencils. Rather than try to explain it and confuse you, here is a self explanatory picture.