Poles are the obvious answer but if you want to go properly stickless there's a trick worth knowing: pitch low and let tension do the work instead of height. On open ground (fells, moorland, dunes) I'll peg the ridgeline out flat-ish between two rocks, a fence post, even a rucksack propped on its end, then use the tarp's own guy-out points with fairly aggressive tensioning to get a stable a frame or lean-to shape without anything vertical holding it up. It sits lower than a pole pitch, which sounds like a downside but actually helps in wind less profile catching gusts, and you're not relying on a single point of failure (pole snapping or working loose overnight).
The other thing that changed my tarp life on open ground was carrying a couple of cheap alloy tent pegs longer than standard (30cm+) for the corner/guy points, since normal 6 inch pegs just don't bite in loose moorland soil or sand. No good having the perfect pitch if the pegs pull on the first strong gust.
Agree with the point above about weight though by the time you're carrying a bivi bag as backup for genuinely open, treeless, pileless terrain, you're often not far off tent weight anyway. I still take a tarp as first choice but always have a bivi as the "what if I can't get a good pitch" fallback rather than trying to force a tarp to work somewhere it really doesn't want to.