On the desktop version of RotaCloud, at the top of the rota, you will see a row titled Open Shifts (provided your account manager has enabled it). These are shifts that haven't been assigned to anyone.
You can claim these for yourself on a first come, first served basis by clicking the shift and hitting Claim Shift.
Once claimed, the shift will be assigned to you on the rota automatically - so make sure you can definitely work it before claiming.
Please note - if clicking an open shift doesn't work your manager may have disabled this feature, or you may not be able to work the role.