How do I enter an expense report into the QB system so I can write myself an expense check?

I can give you the steps to record a business purchase made from personal funds in QuickBooks Online, @usermonica.whitten,

First, make sure your name is set as a vendor in QBO. Since this is a business expense paid using your personal funds, you can enter a journal entry to record the transaction. Here's how:

1. Tap the + New then choose Journal Entry.
2. Enter the correct expense Account for the purchase.
3. In the Debit column, enter the amount.
4. On the second line, enter the Owner's equity or Partner's equity.
5. Add the purchase amount in the Credits column.
6. Hit Save and close.
    

To reimburse yourself for the expense, you can enter it as a check or as an expense.

Reimburse using check:

1. Press  + New then choose Check from the list.

2. In the Payee field, enter the name of the partner/owner.
3. Enter the Bank Account for the reimbursement.
4. In the Category column, select Partner's Equity or Owner's Equity.
5. Add the Amount.

6. Select Save and close or Save and new.
    

Record the refund as an expense:

1. Use the + New icon on the Toolbar.

2. Pick Expense.

3. In the Payee field, add the owner's name.
4. Select the Payment account.
5. In the Category column, choose Partner's Equity or Owner's Equity.
6. Fill out the Amount of the reimbursement.

7. Hit Save and close.
    

You can also refer to this article for the complete steps: How to pay for business expenses with personal funds

If you have any questions regarding the steps, let me know in the comment below. Thanks for visiting the QuickBooks forum. Have a great day!