If the inserts fall out, remove it and carefully scrape the glue off the edges with a knife. Remove any loose debris in the playfield where the insert goes.
I use Gorilla wood glue. The light tan type they sell. I get a rag damp with water and clean the inside edge of the playfield where the insert goes to make sure the wood edge is slightly damp. The Gorilla wood glue needs the wood to be damp to have the glue grip the wood.
Apply glue to the inside edge of the playfield with your finger and also around the edge of the insert. Make sure not to get glue inside the insert. I wait a minute and push the insert in making sure it's oriented correctly if it has text. Clean any glue off the top side if any squeezes out with a clean damp cloth. I run my finger around the edge to make sure the insert is flush. Every 30 seconds or so check again. If the insert feels like it's sinking down too far, reach underneath and push up until it's flush. After about 5 minutes it should be set enough and shouldn't move any more. Keep the edge clean of any glue that may come up.
After about 30 minutes gently get off any glue around the insert edge but don't push on the insert. Let cure overnight. Should be fine 24 hours later to clean and wax.
I had to do a whole Royal Flush that way and it's been fine. Better than having inserts fall out when lifting the playfield.