A stair gate is one of the few pieces of equipment in the house that works only if it is fixed to the right thing. The gate itself is the easy part. The mounting is where the job is, and it is the part that gets skipped when the family is tired and the hardware looks simple enough to trust.
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Measure the opening before you buy
Measure the width of the opening at the top and at the bottom of the stairs, at the height where the gate will sit, not at the floor. Walls are often out of square, and a baseboard, a rail post or a bulge in the drywall can narrow the space where the gate meets it. Write down the narrowest measurement. Gates list the widths they fit, and the narrowest point decides whether the gate fits at all.
Read the label or manual for the mounting types the gate allows and the gap sizes it is designed around. Some gates are rated only for pressure mounting, some only for hardware mounting, and some for both. Do not assume that a gate sold for a hallway doorway is suitable at the top of a staircase.
The top of the stairs is hardware-mounted and opens into the room
The gate at the top of the stairs matters most. Use hardware mounting there, with screws into solid framing or into a newel post that is firmly fixed to the floor structure. A pressure-mounted gate can be pushed out of place by someone leaning on it, and at the top of the stairs that is exactly the failure you are trying to prevent.
Set the gate so that it swings toward the room, away from the stairs. A gate that opens toward the stairs can be pushed open by a person who falls against it.
The bottom of the stairs may be pressure-mounted, if the label allows it
At the bottom, a pressure-mounted gate can work if the label permits it and the floor is level and firm. Check that the gate sits square on the floor, that the tension parts are tight, and that the gate does not rock when pushed. Treat any rocking as a reason to stop and fix the setup, not as a small adjustment to live with.
The mounting job, in order
Find the studs with a stud finder and mark them with painter's tape before you drill. Drill pilot holes, not full-size holes, so the screws bite into the wood without splitting it. Mount the hinge side first and tighten each screw fully, then fit the latch side and check that the latch engages without forcing it. If the only solid point you can find is a post, use the post. If you cannot reach framing or a solid post at the top of the stairs, do not test a new anchor there. Set the gate aside until someone who knows the house can look at the wall.
Test it the way a person would meet it
Push the mounted gate hard from the stair side, pull from the room side, and lean your full weight on it. The gate should not move at the screws, and the latch should close with a clear click and hold. Operate the latch with one hand, the way someone would in the dark or when tired. Check that a person inside the room can open it without a key or a tool.
Name who checks it, and how often
Write down who checks the gate and when. Screws loosen over time, and the ones at the top of the stairs need the most attention. Pick one person for a weekly check of the screws, the latch, the swing direction and the wall around each mount. Record each check on a sheet taped near the gate or in the notebook you already keep for the house. Nothing about this is dramatic, and that is why it gets missed.
When a hired caregiver is in the house
A hired or in-home non-medical caregiver can be asked to look at the gate during the walk through the house and to report a loose screw or a sticking latch. Tightening screws or changing a mount is work for the family or a licensed trade. The caregiver should also be told plainly that the gate stays in place and is not opened or moved for a visitor without the family's say. If the gate is part of the plan for keeping someone safe on the stairs, ask the hospice team what they have seen in the house and what they would want to see at the next visit.
Decide before you drill
Settle where the gate goes and why, who needs to open it and how often, and who owns the weekly check. If those answers are not clear, the gate is not ready to install. The mounting stays in the wall long after the equipment is no longer needed, so settle it first.