The simple answer is that it is very difficult to guarantee safety on a public wireless network, as everything you send can be received by an attacker.
- Configure your firewall to deny any connections
- Strong wireless encryption is a must - if the network offers anything less than WPA2, don't use it.
- Don't use websites that use http - you must use https (which uses SSL) and ideally, check that it is using at least TLS1.0, TLS1.2 would be the best
The thing you can't confirm is how secure the wireless access point is - an attacker could have control over it, which means the wireless encryption is not protecting you.
So you should really use a VPN for anything sensitive or valuable, so you have an encrypted tunnel to an endpoint not attackable at your location.
And if you are working with really sensitive information - just do not use any public wireless network.
Know the risks and decide. Are your bank account contents valuable to you? If so, you may not want to do online banking on a public wireless network anyway.
There are loads of questions on this topic over on Security SE, so if you want more information please have a look.
2“Strong wireless encryption is a must” No, it's useless for the user. Encryption or the lack of it concerns the hotspot owner to authorize connections. When you don't trust the network infrastructure, it doesn't matter whether it encrypts anything. – Gilles 'SO- stop being evil' – 2013-02-19T09:38:02.070
1Defence against different attackers. strong encryption - against others on the network. But defending against an attacker who owns the hotspot.....nah, that's a trust issue – Rory Alsop – 2013-02-19T09:39:36.207
1How do you know whose hotspot you're really connecting to? Anyway, regardless of how much security it provides (some, but not enough), it's useless because you can't rely on it, hence the need to use encrypted and authenticated protocols (SSL) anyway, hence additional cryptography in the network is irrelevant. – Gilles 'SO- stop being evil' – 2013-02-19T09:44:00.160