There is no single answer for the best way to get to know your new city, just many suggestions and online findings. If you do a basic Google search you will get some predictable results – the wiki page, the current news, trip advisor, and more travel related links. Wikipedia is a good place to start for basic information (as with most topics) and wikitravel is surprisingly comprehensive. You can buy a country or city guide, with Lonely Planet being the most popular, or you can just check out their website – they also feature a useful forum.
Another great forum, travel community (and much more) is couchsurfing. You can find other travellers, expats and locals who are looking for new friends to check out local happenings.
There have also been some shifts away from the giants of travel (like Lonely Planet) to ‘local’ guides, because nobody wants to fall into the tourist trap, right? Like a Local, Spotted by Locals, and With Locals (not free) are some examples.
Or, you can find personal blogs. Sure, blogs can be incredibly subjective but don’t discount them because they can offer some great insights into specific details that websites might not include. Reading a good blog can be a vicarious experience. You can just Google ‘city name + blogs’ or you can use Technorati, a blog database, to find what you’re looking for.
But most importantly, when you’re in your new city, get out there are EXPLORE!