IF you are using 1/2" drip tubing (thin stuff to allow emmitters to be punched into the tubing), then the maker of your tubing likely makes a connector to transition from hose spicket to tubing. Usually, this is a part of a set that would include a pressure reducer, a simple backflow preventer, filter, and 1/2" tubing connection that all connects up to your hose spicket.
The transition of 1/2" tubing to 1/4" tubing is done via double barb fittings. The 1/4" tubing slides over one barb, and the other barb is punched through the 1/2" drip tubing.