There are two ways of filing a claim –
You can show your card at a network hospital or clinic. The hospital or clinic will claim the expenses themselves, and you don't have to bother with the claims process. You don't have to pay upfront in these cases unless your medical insurance policy doesn't cover the procedure or you may have to co-pay a certain amount.
If you choose to get treatment at an off-network clinic or hospital, for whatever reason, you will have to pay upfront. Later you can file a claim by submitting the receipts to your insurance provider. They will assess your plan and reimburse you accordingly.