Without seeing the pattern it's difficult to say, but if it's a patchwork pattern in a standard size (6 inch block, 8 inch block, 12 inch block), you only need a calculator and a measuring tape.
First, determine the dimensions of the queen sized quilt by taking the mattress size and adding what is needed for the quilt to drape over the sides, the foot, and any extra you want at the top. 88" by 108" is a common queen size but you can measure a store-bought coverlet that is the right size as well.
Then, do the math to increase the number of blocks from twin to queen sized.
Let's say your pattern has 12 inch blocks and a four inch border all around. Subtract 8 from 88, divide by 12, and round down. You will need six blocks across.
Subtract 8 from 108, divide by 12, and round down again. You will need eight blocks across. 6x8=48 blocks to make the queensized quilt. You can increase or decrease the border size to make up any small difference in size.
Check out your local library; any standard how-to book on quiltmaking will have more thorough instructions.