The column method and the grid method, both worked out on your own numbers
Long multiplication is not one calculation, it is a handful of small ones added together. This shows both standard ways of laying that out on whatever numbers you enter — the column method, which stacks partial products, and the grid method, which splits both numbers by place value first. Neither is better; they are the same arithmetic arranged differently.
Multiply the top number by each digit of the bottom number in turn, starting from the units, shifting each partial product one place further left, then add the partial products together.
Because that digit stands for tens, not units. Multiplying by the 2 in 23 is really multiplying by 20, so the partial product is ten times bigger and shifts one place left.
Split both numbers into their place values — 47 into 40 and 7 — multiply every part by every part, then add all the products. It is the same arithmetic as the column method with nothing hidden.
Estimate with rounded numbers to check the size, and check that the last digit of your answer matches the two units digits multiplied together.
Yes — every partial product is a times-table fact. If those are slow, long multiplication is slow no matter how well the layout is understood.