What to Say
The arrangements of visitations and specifics of your particular divorce situation will alter the script of this conversation, but here is a general guideline. (Remember, young toddlers need language to be short and simple, and what you say will need to be appropriately repeated for your child to begin to understand.)
Mommy loves you and Daddy loves you very much. But beginning today, Daddy and Mommy are going to live in different homes, Mommy in one home (or house or apartment, depending on familiar language of child) and Daddy in another home.
You will live with Mommy at home and see Daddy. Mommy will take care of you feed you, hug you, give you kisses and put you to bed. Daddy will take care of you feed you, hug you, give you kisses and put you to bed.
(Toddlers don't grasp the idea of time yet, so telling your child that she'll see Daddy on Tuesdays and Thursdays isn't especially meaningful. You can let your toddler know about a confirmed visit on the same day it's happening.)
Keep in mind: New experiences increase anxiety in young toddlers, so repetition and consistency of the visit routine will increase your child's familiarity (and decrease his stress) over time. Once he is familiar with going to the other house, you can reference "Daddy's home," and as your toddler develops he will begin to understand where that is.
Toddlers will however, need to actually see the house to begin to understand where they're being taken to. It can be helpful to give details about the house once they have been there: "Daddy's house is next to the store and playground," but this understanding will emerge more fully as your child gets older.
What To Do
Repeatedly reassure your toddler. Separation anxiety is a normal part of your child's development at this age, and it may increase during the early days of swapping homes. Run through your script as many times as it takes for your child to begin to internalize that she will, indeed, be taken care of and see both parents.
Keep routines as regular as possible. When possible, have conversations with your ex about maintaining routines, as toddlers thrive on them. If conflict between the two of you is too high to nail down consistencies, focus on what you can do at your house to keep routines consistent.
Spend extra time with your toddler and give extra affection, expressions of love, and reassurance. Toddlers regulate anxiety through their relationships with their parents. Leave extra time to complete routines.