1. Always analyze the problem first. You should always check what the exact problem is and what is the effect.
2. Find the root cause of the problem by checking the relevant log files or the event viewer.
3. If there is any specific error or warning found at the particular time when the problem has occurred, then find details of the event. You can use Google effectively to search the reason by using the event log entry as the search string.
4. There may be multiple different causes found if the event log entry is generic. Try to find the relevant solution according to the server or the application.
5. Use tools like ping, nslookup, dig, telnet etc., as per the issue's nature.
6. Always post the issues you are facing in relevant discussion forums if the solution is not found.
7. If there is support available from the vendor, then make full use of the support facility to resolve the issue. The solution in this case may take some time, but in case when the solution is not found easily, you can always contact the vendor to get the issue resolved.

Using the above method, you can resolve lots of issues easily.