Apply a layer of compost under the tree each spring, spreading it out to the dripline (the area under the outermost branches). Add a 2-inch layer of mulch to retain moisture and control weeds, keeping mulch a few inches away from the tree trunk. Water plants during the summer if rainfall is less than 1 inch per week. Flowers are produced on new wood, so prune back weak, spindly growth in spring to encourage better flowering. Prune off dead, diseased, and broken branches anytime.
Crepe myrtles can be propagated using pretty much every method out there. Cuttings, divisions, seeds, and layering all produce good results.
For seed starting, stratify seeds for 60 days. Best results can be had using the paper towel method. Sow seeds into a paper towel inside a plastic zip-top bag, moisten and place in the fridge for 2 months, then place the bag under growlights. As soon as the seeds sprout pot them up into 4" pots. Transplant into the ground once nighttime temperatures stay above 50 degrees. Seedlings started in the spring will often bloom during their first year.
Crepe myrtles have a habit of suckering - putting up new shoots out of the ground. With most varieties, you can carefully dig out these suckers along with some roots and have a new plant.
Softwood and hardwood cuttings both work fine. Rooting hormone and frequent misting dramatically improves cutting success.