Networking isn't hard. It's discipline which becomes habit. It also isn't relegated to events only. You are probably already networking and calling it something else.
Networking is simply connecting. How deep you wish to make a connection is up to you. Ample opportunities to connect appear every hour. You don't have to seize each one - you should be at least open to the possibilities presented.
And being mindful of the things below may not solve how to 'work a room' but it does make talking to strangers more of a regular occurrence in general.
It's all choice.
1 - Everyday I say “hello” to people - my neighbours; their kids; my co-workers; people emptying my garbage cans, etc.
2 - After I say “hello”, I listen to the response - sometimes even have a brief conversation.
3 - I make eye contact - even briefly - entering elevators; walking down the street; with store clerks - this can result in more of #1 - 10.
4 - I say “thank you” - to people holding doors; processing my requests; bagging my groceries; giving me feedback; etc.
5 - I apologize - when I’ve made a mistake; forgotten something; been inconsiderate.
6 - I follow up on calls and emails - to acquaintances; friends who wait patiently for me to get my schedule together; requests in or out; etc.
7 - I offer thoughts and perspective - offers of help; random compliments; timely critiques; etc.
8 - I keep my calendar up-to-date and block time throughout the month for informal coffees and email catch up. (if I don’t need the time, then I have free time)
9 - I try not to rush in and out of every room, meeting and encounter so I appear approachable.
10 - I keep a sense of humour and look for like-minds who do the same and make sure I follow #1-9 with them when I find them!