Basic abacus as a manipulative
I don't mean a Chinese or Japanese abacus with a special counting system. I am talking about using a simple 100-bead abacus for counting, and treating each bead as 1. You don't have to learn any of these sophisticated systems that have been in use with various abacuses. Just consider each bead being 1, period.
Then you have 10 tens, or a hundred, in your abacus, and that goes a long way explaining tens and ones or 2-digit place value to first graders.
Then the child will easily recognize 6, 7, and 8 beads without counting. Also, let's say you choose 6 beads on one wire and 8 on the next one. You can show how the five and five on those two wires makes ten, and some are left over.
To help a child learn the numbers up to 100, you can play a simple game with the abacus. When it's your turn, you say a number, and the child "makes" it or shows it on the abacus. Then your child says a number for you to show on the abacus.
You can also show the child other things, such as how the subtractions
10 − 5
20 − 5
60 − 5
are similar, or let the student find sums of 2-digit numbers, such as 23 + 45. He can move 2 tens and 4 tens, then 3 and 5 individual pieces — you can show how to add the tens and ones separately.
You can let the child explore what happens with 28 + 9.
You can also model multiplication: move 4 beads on each of the 5 neighboring wires, and there you have 5 times 4!
Browse Amazon's abacus selection here.
So this is not rocket science; it is very easy. You don't need to learn any special abacus systems.