A 2 to 3 inch layer of an organic mulch offers many benefits to a tree. Spread directly on the soil under a tree, wood chips, shredded bark or chopped leaves discourage weeds, insulate the soil from temperature extremes, absorb and retain moisture and protect trees from injury by lawnmowers and weed trimmers. Spread the mulch in a circle around, but not touching, the trunk out to the dripline. This will also eliminate competition for soil nutrients from lawn grass growing over the roots.
Most trees require special attention to watering when they are first planted. Sycamores, especially, like moist soil, so try to assure that young ones get at least an inch of water a week from rainfall or from a watering system.
After their first year in their permanent site, young sycamores benefit from annual fall feeding for a few years. Sprinkle all-purpose slow-acting granular fertilizer on the soil under the tree out just beyond the reach of its branches (dripline) for the rain or watering system to soak in. Use about 1/2 pound of fertilizer for each 1/2 inch of trunk diameter, measured at the base. As long as the tree is not growing in turf, which competes with tree roots for this nutrition, this will be sufficient for the season.
For more information see the files on Fertilizing Trees and Choosing Fertilizers
Mature sycamores generally present sturdy resistance to winter winds and ice. However, in the Midwest there have been problems with frost cracking of sycamore trunks. It may be wise to shelter newly planted young trees that are in exposed sites behind a screen of burlap or agricultural fabric during the winter. Do not wrap trees, and never use plastic, because plants need air circulation to remain healthy.
While sycamores do not require routine pruning, they occasionally need pruning to maintain a single central stem, or leader, when they are young. They also benefit from periodic trimming in their formative years. They respond so well to even hard pruning that they are often groomed as hedges or shaped to make allees. In residential yards, most likely it will be necessary from time to time to trim injured branches or ones that grow so low on the trunk that they obstruct passage through the yard. Judicious trimming of secondary branches also will encourage maximum development of main branches as the tree ages. Use a sharp pruning saw or loppers when pruning and wear a protective dusk mask to avoid irritation from the fuzz that forms on sycamore leaves, fruits, and young twigs.
For more information see the files on Pruning Shade and Flowering Trees and Choosing Pruning Tools