An addition to Kilieni's guide. Covers the more recently discovered movement glitches and how to combine them effectively.          This guide does not include the Out of Bounds movement glitch.
Extended Movement Glitch : This trick was shared by NoWorries. You can half-step off any friendly character, open the menu, close the menu, continue to menu buffer and walk along your movement range to reach an extra space. Additionally, if your half-step is centered in the middle of the tile, you can walk forward in the direction you are facing to move an extra tile outside of your movement range without needing to pass through an ally. After a half-step you never face upwards or left, so you can't directly walk forward in those directions.                                                                                                                                                                                                                                                               Slingshot : The slingshot is a glitch discovered by NoWorries that utilizes half-step movements to place your character onto the edge of a tile, followed by rapidly pressing the menu button(s) while moving forward to gain a burst of momentum. This will push you through allies and enemies that are lined up together, potentially allowing you to move multiple tiles past your legal movement range. Unlike the basic movement glitch, you can slingshot left and upwards. If you slingshot an ally left off the screen, the game will softlock after ending your turn.
Minimum Half-Tile Position : The easiest way to setup a slingshot without needing another character on an adjacent square is to half-step in any direction, close the menu and quickly half-step again. You can keep half-stepping to move along the border of any movable tiles that another ally or enemy is connected to. Difficulty of this trick depends on how precise your controller is. If you are playing console and are having trouble with a used Model 1650, try replacing the old conductive pads with new ones.
Extended Half-Step + Slingshot Combo : By placing a single character as an anchor to achieve the proper half-tile position, you can use the extended movement glitch to move through enemies and slingshot through another line of enemies. This example avoids enemies from surrounding Peter or blocking his path, and still gives him the range to kill the Soldier on turn #3.
Slingshot + Half-Step // ¬ Slingshots : Since slingshots are just an extension of the basic movement glitch, you can combine them with half-steps to move in a right-angle formation. When mashing the menu button(s) during a slingshot, change your direction the moment you start moving between two allies/enemies.