Some people ask me how to apply SAP patch level on Production SAP system. Actually it is possible. But it is high risk task. It is better you apply them when no user is logging in to your system.
OK, here is the step by step.
1. Make sure that you have download all SAP patch you need to be applied.
2. Apply SAP Basis Component (SAP_BASIS - usually named SAPKBxxxxx) and Cross-Application Component (SAP_ABA - usually named SAPKAxxxxx) first. And also from my experience and some best practice, apply them on the same patch level. For example when you're applying SAPKB62059 then apply SAPKA62059 too.
3. Consult to your functional consultant and functional team before applying Logistics and Accounting component (SAP_APPL - usually named SAPKXxxxxx). I repeat this warning again. Consult first before applying because this patches will affect to your customizing setting. If you're not sure about this, then don't apply them.
4. Use DDIC user to apply and login to client 000. Start from your Development server.
5. Last thing, pray...
I hope this few tips will help you.