I rarely do. When I have to (or want to) I ask a relative or a close friend of mine. Usually my brother. I think in the last ten year I haven't made more than ten online purchases.

So... Not owning a credit cart isn't (for the moment) an inconvenience for me because I rarely need to use one and if I have to I can find someone to help me with it.

I pay my bills via the online banking system my bank set up though. I use a card (one issued by my bank to each of its clients that allows me to pay for stuff IRL or to retrieve cash from ATMs) with a little calculator-like device that churns out temporary authentication codes. This system only works with my bank though ; I can't use it to buy from online vendors[0]. But I don't think it qualifies as online purchases. It wouldn't let me buy hosting for instance :)

[0] there are some exceptions though. ie mobile company generates links that initiate a transaction I have to confirm via the calculator and by logging into my bank.