What you need to match is the guage given in the pattern. It may be the same as listed on the yarn band, but quite possibly not. If the pattern tells you that 25 stitches = 4" using size 7 needle, that's the stitches per inch you need to match with the yarn you want to use.
You may need to use a larger or smaller needle, but start with a 7 needle and your new yarn, cast on 35 stitches and knit for 3-4 inches. then measure and see how close you are to the pattern's guage. Change needles if necessary and knit another 4 inches, measure again. If you can match the guage, you are good to go to just follow the pattern directions.
If you just can't get the same guage, it could still be possible to use the new yarn. It may require major math to make it work. Or it could be as simple as making a different size.
Also depends on just what you are making. If it's clothing, something that needs to finish to a certain size - then it's very important to match the guage. If it's a blanket, purse, or somthing like that, it may be no problem if the finished item comes out smaller or larger then the pattern design.