They are very specific in their drinking requirements. Those little umbrellas, shot glasses, and tiny straws were made specifically for giving Praying Mantises a drink. They take their water neat, umbrella to the left, straw to the right.
Many have reported that their mantises take water through a process called "misting", but the Mexican Beach Mantids, occasionally seen at Phils place in Yuma, AZ, refuse this method.
But other than that species I would go with misting first, if that doesn't work, try the above method. And if they don't drink when you mist them, they probably aren't thirsty or can't get to the water.