Two connected pawns supported by the king win easily. Advance them side by side, keep the king in front of the enemy rook's checks, and use your own rook to drive the enemy king away.
With two connected pawns against a lone rook the win is straightforward, provided the pawns do not get separated and the king stays with them. The technique is to push the pawn that the enemy king does not block, and to use the king to shut out checks.