You are putting up a shelf so the supplies come off the dresser top and the bedroom floor. It is small work, but it has an order, and the order is what keeps the shelf on the wall after the first load goes on it.
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Pick the wall before you buy the shelf
Choose a wall you can reach from the bed without stepping over a cord or a rug edge. Measure the clear length between the door swing and the nearest corner, and make sure the shelf will not sit where the bed, the door or the bed controls need to go. Note the wall type. Plaster over lath and drywall take different anchors, and a wall you cannot tell apart by tapping is a wall to test before you drill.
Find the studs and mark them
Run a stud finder across the wall at the height of the bracket, then confirm each stud with a small pilot hole that the bracket will later cover. Mark the stud centers with painter's tape rather than pencil so the marks come off clean. Measure the distance between the two studs you will use and compare it with the bracket spacing before you drill anything large.
Set the anchors and hang the bracket
Use wood screws long enough to reach solid framing when the bracket sits on a stud. If the bracket must sit between studs, use the anchor the bracket maker lists for that wall type, not whatever is in the drawer. Set the bracket level using a level on the top edge, tighten the screws until snug, and stop before a screw head sinks into the wall material.
Load-test before the supplies go on
Place one light item on the shelf and pull down on the front edge with a steady hand. Wait a while, then look at the bracket and the wall again. Add weight in steps, not all at once. Do not exceed the weight the bracket maker publishes, and count the weight of the containers, not only the contents.
Name who checks it
Write on a note in the folder who looks at the screws and the level, and how often. Check the screws after the first week and again each time the shelf is moved or restocked. The shelf holds supplies. Decisions about where medicine is kept belong to the family, the doctor and the pharmacist, and the shelf plan should leave that to them.