There are probably many ways to get to this cache. I will describe the route my friends and I took so you can follow it if you want. We intentionally chose a route that involved rappelling, scrambling, and rope ladders, because that's what we enjoy. You may be able to find something easier, but I wouldn't count on it.
Starting from the indicated parking spot, we headed down canyon, quickly getting into the gypsum or alabaster layer where the canyon began to get deep. From here on there are only a few good places to escape the canyon that might provide alternative routes in. We followed as the canyon cut down through the alabaster until it reached the top of the Entrada Sandstone layer where there is a 60 foot rappel. I'm told it's possible to scramble around this cliff on the right side looking down canyon. We saw bear and mountain lion tracks in the mud below the rappel.
The canyon walls become alabaster again, as we must have crossed a fault. Sometimes the canyon is quite narrow. Then sandstone again with occasional small climbing problems, including one where we used a 15 foot rope ladder so we could get back up on our way out. Eventually we came to a place where the canyon dives 30 feet into a narrow deep slot, and used another rope ladder here. This slot is the highlight of the whole trip, however you don't need to descend into it to get the cache.
From the top of the 30 foot drop into the slot, go back up stream 20 or 25 yards, then climb up to the base of the wall on the left looking up stream (southeast side of the canyon). The cache is under a couple rocks at the base of the wall.
I highly recommend continuing down through the slot to the Gallina River, as this is the most interesting part of the canyon. But if you don't have the equipment or skills to do so, the rest of the canyon is still very much worth a visit. If you attempt to approach this cache from the bottom, good luck, I didn't see any way I could get up that 30 foot drop without having left a ladder there on our way down.