Most productive method for us over the years has been trolling. Nearly anything can work at given times, though my personal preference are slim bodied minnow type lures that run shallow to mid range when trolled.
Lac St Louis has been good to us over the years, many overlooked areas are home to some of the system's biggest walleye, which typically feed heavily in the spring. Covering lots of water by trolling is by far the most effective method this time of year, my kids land some nice walleye trolling every spring.
Trolling shallow can be productive as well, these big walleye were caught trolling worm harnesses right at the surface over 11 feet.
Casting for walleye is often overlooked. Walleye often hold near transitions from shallow to deeper water in spring, so casting shorelines from boat or while shore fishing with crankbait or jigs does the trick quite often.
Hope to get out for some walleye fishing soon, as I haven't targeted them since last summer.