Launder the linen items in a washing machine. Add an appropriate amount of mild laundry detergent, set the water temperature to warm and the wash setting to gentle with a low spin.
Remove the items from the washing machine after the cycle finishes and transfer them into the dryer.
Set the dryer to low heat and a gentle setting. Allow the items to dry completely or remove them while they remain slightly damp and then iron them.
Set the iron to a medium-high setting. Iron the linen items on the back side of the fabric to remove wrinkles. Ironing linen on the back prevents a sheen from developing on the front of the fabric. Identify the back by finding any hems -- the seams of the hem will face the back. In the absence of hems, examine the linen carefully. You'll notice a smoother surface on the front. In addition, linen fabric typically comes folded on a bolt with the front facing out.
Repeat the washing, drying and ironing process until the linen develops the softness you desire. Every time you wash and dry linen, the fibers soften.