Wi-fi issues are not unique to Symbian, of course. I've seen Android and iOS message boards complaining bitterly about Wi-fi with each OS, either with a specific device or a specific device update. But I know Symbian well enough to suggest a possible work flow for looking into any Wi-fi issues you may have. See what you think - can you add any more steps/suggestions?

First of all, by 'issues' I mean any problems which get in the way of normal operation. Perhaps the connection can't be made to your router in the first place, or perhaps the connection starts OK and then drops randomly?

In approximate order of suggestion (i.e. start at the top and work your way down, testing as you go - and stop when things seem to be fixed!):

1. Check your device has the latest firmware and SW_update patches. Wi-fi issues have been fixed in several updates over the last few years, so triple check you're up to date here. I'm assuming that, even with Wi-fi issues, you have some means of updating. Perhaps via cellular data? Or via plugging into a Windows desktop/laptop and using Nokia Suite?
     
2. Try restarting your router (i.e. power it off and on again). This sounds obvious, but most people treat a router as a) infallible and b) an appliance that should be left on 365 days a year and never touched. It does a router good to be restarted every now and then (clears out its device tables, etc.) and, in some cases, if you leave the power off for a minute or so then the router automatically checks for updates to its firmware when it's powered on again (if this isn't the case for your Wi-fi router then consult its manual or manufacturer for the approved way of logging into its control panel and checking for updates).
    
3. Check that your access points make sense and are in the right order. You should see just one main group, entitled 'Internet' and then, within this, your frequent Wi-fi access points listed at the top, with any cellular ones below them in the list. If any are out of order then long press and 'Change priority', then tap where you want them to go.
    
    
     
4. Obviously, you'll have tried powering the Symbian smartphone off and on again. But it's also worth deleting the Wi-fi entry for your router in Settings>Connectivity>Wi-fi - just tap and hold and then tap on 'Delete [Wi-fi access point]'. Leave it a few seconds and then tap on your router SSID/name again to set it up as a new connection. If something's changed in your router then refreshing the connection in this way may just get the phone and router back in step.
    
   
   
5. Check that your Wi-fi settings are 'correct'. You'll find these in the same dialog (Settings>Connectivity>Wi-fi) but then tap on the Options menu and choose 'Settings'. Depending on your smartphone and version of Symbian, you'll see one or two options: 'Power saving' and 'Advanced power saving'. BOTH of these should be 'enabled'. One misconception is that Wi-fi drops are caused by power saving cutting in, but that's not the case. Power saving merely intelligently manages the power of the connection so as to help save battery life. 
     
6. There's a strange bug in Symbian which can occasionally interfere with Wifi. Look in Settings>Connectivity>Admin.settings>Mobile data. If you're having Wi-fi issues and the 'Access point' field says 'None' then try typing in 'Internet', to match the destination in Settings>Connectivity>Settings>Network destinations.
    
   
     
7. Try changing the 802.11 'mode' of your router - try 'g' (up to 54Mbps) if you're having trouble with 'n', etc.

Hopefully working through each of these will have got you up and running again. 

Comments welcome. Can you think of any other Wi-fi troubleshooting measures for Symbian? Please share!