Variety -- #1 tip -- if you want a larger hosta leaf, get a hosta that has naturally large leaves. Top "large" varieties I love include; Blue Angel, Blue Mammoth, Empress Wu, Komodo Dragon, Sum and Substance, and T Rex.
Planting -- Plant in super rich, organic soil. Amend soil if needed - my favorite amendment for hosta is composted manure.
Feeding -- Test your soil and see what the soil is lacking - add as recommended. Hosta plants like to be fed and adding blood meal fertilizer to the soil on top of your traditional organic fertilizer amendments surrounding the plant will give it extra nitrogen. This nitrogen will help the leaves get and stay larger.
Schedule -- Fertilize at the first of the season, then again a second time 4 to 6 weeks after the leaves emerge to give the leaves an extra nudge
Watering -- Water regularly at the base of the plant. Hosta survive well in drought and I rarely water the plants, depending on Mother Nature to water them with rain. However, once in a while I want to give a hosta a growing boost. Drown the plant thoroughly once a week with a heavy watering. I water until the ground is saturated, then come back with a hose two hours later and water again until the ground is saturated again. Wait a week, then repeat the process.
Light -- While hostas are known as shade plants, they do indeed like sun. Full sun will burn the plants leaves in the heat of summer. Part sun or part shade will do very well for a hosta and you will notice that the leaves get larger in a semi-sunny location if it is regularly watered and fertilized. Prevent leaf scorch by giving it more water than if it were planted in shadier spots.