Your cousin has to ship them to an FFL (licensed dealer) in TX, who will then transfer them to you (on a Form 4473 and with a NICS check). Alternatively, your cousin could bring them to a TX FFL who would transfer them to you.
Try to find an FFL close to you who doesn't charge too much for handling the transfer. Long guns can be shipped by USPS (only an FFL can ship a handgun by USPS). FedEx and UPS will ship either, but usually they must be taken to a main hub (not a suburban Kinkos or "self ship" location). Generally, the carrier requires that handguns be shipped by overnight priority. That costs a bit, but the shipment is carefully tracked.
Send lawyers, guns, and money...
(Formerly known as "Henry Bowman" on THR)