You may drill anywhere along any edge of your remote, but the bottom rear edge will probably be the best spot for most remotes. It would be ideal to drill at a 45-degree angle to maximize the plastic material's strength. Also, drill about 1/8 " away from the edge to leave enough plastic material to form an unbreakable anchor. If you start your 45-degree-angled hole 1/8th " from the edge, the angled hole quickly thins the material left on the corner edge. So be careful not to make your anchoring edge too thin.
Step 1: Attach Lanyard
Thread the thin looped end of your lanyard through the hole you just made. Pass the looped end around the edge and over its opposite side the to create a tight cinch. You're done.
Step 2: Variations
This design is not finished. I'm still considering adding different items to the lanyard to make it pop out more. My first thought was to attach a tennis ball to the lanyard, but we have an indoor dog, so that idea was out of the question. However, now I can easily add handkerchiefs to the lanyards if I decide, but I don't think they are needed. I want to make the remote finders 3-D without adding too much bulk or weight. Jingle bells can add sound effects to help in locating them. You may choose to tie your remotes together with their lanyards, or use the lanyards to hang them up on the wall. The possibilities are endless now..