Make teleporting a mode of movement
There is no standard wording for expending movement to teleport. However, the basic movement rules already allow for different modes of movement:
Your movement can include jumping, climbing, and swimming. These different modes of movement can be combined with walking, or they can constitute your entire move. However you're moving, you deduct the distance of each part of your move from your speed until it is used up or until you are done moving.
If the ability makes teleporting a mode of movement, then the rest of the movement rules should work properly. Such an ability could be worded like this:
You gain a teleporting speed equal to your walking speed. Teleporting is a mode of movement for you. You may instantly teleport to an unoccupied space you can see as part of your move, deducting the distance teleported from your speed as normal.
The creature could then use their teleporting speed in every situation that they would use their walking speed, including moving between attacks. If the creature also had a flying speed of 60 feet, they could teleport 30 feet, then switch to flying as normal.
Consider what side effects you do/don't want
Since teleporting is based on your walking speed, a creature that is grappled or restrained will be unable to teleport. If you want to avoid that, your teleportation ability will also need a specific rule to override it:
Your teleportation speed is not affected by being grappled or restrained. It remains equal to what your walking speed would be if you weren't grappled or restrained.
Teleporting in this way would technically trigger opportunity attacks+. If you want to prevent that, you could add something like:
When you leave a creature's reach using your teleporting speed, you do not provoke opportunity attacks.
+ Credit to Revolver_Ocelot in the comments.