In the British English world, in this context, "a mobile" is a short way of saying "a mobile telephone". In the USA, "a cell" is readily understood as meaning "a cellular telephone" or "a cell phone".
Having disposed of that issue, we come to the topic at hand. Where I come from, there are a number of ways of getting a mobile phone:
1. On a monthly contract: you enter into a contract with a mobile phone provider, and get a handset. You pay a sum each month for a fixed period - commonly 12, 18 or 24 months. The monthly sum covers the cost of the phone and also a certain amount of talk time, text messaging, and data usage (the 'tariff'). At the end of the contract period the handset becomes your property. If you break the contract early, there is an 'early termination fee' which enables the phone service provider to recover the cost of the handset. After the contract ends, you can upgrade the phone and start all over again, or else use the existing phone on a cheaper contract.
2. SIM-only deals. You buy the phone (or you have an out-of-contract one) and pay a monthly sum for a set amount of airtime.
3. "Pay as you go" - (PAYG) with this method you buy the phone outright; it is your property and you thereafter buy airtime as you want. You pay money for this, in advance, to the mobile phone company; they usually issue you with a card that has a magnetic stripe, and also the phone number printed on it. The card only exists as a aid to payment; it is not necessary; you can use the card at many shops to buy more airtime (the shopkeeper swipes it in the till) or you can do it at a suitable ATM by inserting your bank credit or debit card and selecting "mobile phone topup" and then typing in the phone number. The topup amount is debited from your bank account. You can also register a debit or credit card with the mobile phone company and request a topup by sending a text message.
So, WBYeats, the answer to your question is that where I come from, the process of paying for more pay-as-you-go airtime is called "topping up" your "airtime balance" or your "pay as you go balance".
Quote:eg I need to ... my phone.
I need to topup (or top-up) my phone.