Most configurations are such that if you slide fully open the window and then slide the screen an inch open, you can grasp the left and right vertical (stanchions), lift up firmly, and then pull toward you at the bottom until the bottom horizontal frame member clears the channel, the screen easily is removed.
Replace it by inserting the top horizontal, press up firmly, and push the bottom frame member in and down in its channel.
The two spring tensioners are in the top horizontal, so lifting upward is the required pressure.
Small slideout windows on the other hand have one set of spring fingers along one side, requiring pressure in that direction to release the opposite stanchion from its track.
Joel