Your going to need to go pick up a dryer vent siding block with the J moulding trim built in.
The siding is removed in the area where the vent is going to be.
Use a long drill to drill a 1/4 hole from the outside all the way through the wall so you can see where it's going to come out to double check there's nothing in the way.
It's best to use a 4-1/2 hole saw to make the hole from the outside, once it breaks through clear the plug out of the hole saw reach inside the hole and clear the insulation out of the way. Then go inside and make the hole through the sheetrock.
SLide the vent into the hole from the outside, check it for level and nail it to the sheating.
Now the siding can be reinstalled, leave about 3/8 all the way around the siding block so the siding has room to expand and contract.
And no you can not leave the siding in place and just cut a round hole through it.