Well welcome to gardening and I love that you are up to the challenge. I suspect your plum tree had a leaf blight or fungal infection brought on by lots of rain. Nothing you can do about the weather but to make a healthier tree you should cut off any dead or diseased branches starting at the bottom and removing those branches that are sticking out from the trunk with no leaves on them. Next add a mulch or layer of bark chips or wood chips on top of the soil around the base of the tree. This will keep the roots from drying out in the summer sun and keep down weeds. A mulch on top of the soil will also seal in any fungal spores that have dropped to the ground. The mulch or wood chips should be 2 to 4 inches deep. Now the big question is will you make the effort to contact a local Master Gardener or nursery owner to show any leaf damage to a local expert. I may not know about a local disease or insect problem specific to your area and local fruit growers are better equipped to solve fruit tree problems in your area.