You must file a Maryland nonresident tax return to get a refund of your taxes paid to Maryland. You can file both the Maryland and Virginia now (at the same time).
For the Maryland nonresident return, choose to e-file and on the following screen elect the option have your refund deposited to your bank account, if possible. That is the fastest way to get your refund.
For the Virginia resident return, choose to e-file and on the following screen elect the option to "pay by check", and then pay the tax due before the June 1st deadline. See the Virginia Tax website at this link for payment options, including an online payment option or the address to mail your check.
And, remember to contact the payroll department where you work to get your state withholding changed to Virginia.
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