The ultimate purpose of your website is to generate income, one way or another. Whether the site is new or a few years old, if it doesn't make you any money, something has to change. Here's a list of 5 proven ways you can monetize your website:

1. Google AdSense
This is probably one of the easiest and most common ways people earn money on their websites. After you make a website, your time and effort should go into creating a lot of high-quality, unique content. You can concentrate on only one topic or more, it doesn't really make too much difference (but don't write about a hundred things, either!). Make sure that you have audience for your site.
Writing the content so it's SEO friendly is a great thing, because it will help you bring more traffic, thus earning more money. Follow these rules for more success:
a) Never put too many Google Adsense units (3 per page) on the site. Concentrate on the more expensive keywords instead of many cheap ones. Your site will look more professional this way, too.
b) Do your advertisements look like ads? Fix that. Blend the site content with the Adsense by using similar fonts and colors.
c) It's never a good idea to run sites for the sole purpose of generating money from Google AdSense. Put some effort into the site, invest in web design and great, compelling content. It will be worth your time and money.
d) Your CTR (click-through rate) will greatly depend on your target audience profile. People who spend more time on the web and know more about the Internet tend to click less on the ads.
e) Check out Google's tips and advice on Adsense optimization.

2. Affiliate Programs
You get paid commission when your visitors perform an action on someone else's site. Negative side of this model is that generating money can be very hard since you only get paid when one of your visiors purchase/register/subscribe to another site. Visitors don't often perform actions from affiliate banners, but there are some things you can do:
a) Concentrate on brand related keywords which often convert very well.
b) Try to make a unique page for every affiliate product you promote. Make it look professional, different and compelling.
c) Find things that are easy to sell. This might take a while, but it will be worth it.

3. Display Ads
You can sell ad space directly on your website. For this model, you will need a website that has a dedicated following. If you pay attention, you will find that many websites on the web do this. Follow these simple tips that will help you sell ad space better:
a) Selling your first ad will always be the hardest. It might take some time, and the best way is to promote 1-2 ads free of charge. This way, you'll have some social proof of value, and ad buyers will feel more comfortable giving you a chance.
b) Be careful when setting the price. Do some research before you even find the first ad buyer.
c) Don't overkill. If your site looks like a disco ball, it's time to stop.

4. Selling Products/Services
This is the hardest, but also the most generous way of monetizing your website. It takes a lot of research, effort and hard work.
First, you have to research the market and figure out what's missing. If you're planning to sell services and products in the market already over-saturated, you're on your way to the dog house.
Recognize a problem, find a solution and make money off of it. Sounds easy, except that it's not. I believe that the hardest part is to recognize a problem that needs a solution. Make people's lives easier and you're going to win. It goes something like this:
a) You have to recognize a demand for something, find a problem that longs for a solution. Go online and ask your prospective customers what bothers them, what would make their lives easier. It might be a simple 30-page e-book about growing the best organic tomatoes or a unique hairclip that is both stylish and effective.
b) Figure out the price of your product or service. This also demands for some research. Reach out to your prospective customers and ask them what they think - how much would they be willing to pay for what you're offering?
c) You have to establish trust. Having logos from BBB or Truste can help you in this. Don't forget to put your name, address and phone number on a visible part of the site. Include your biography, anything that will help your customers establish trust and get to know you better. Post testimonials (don't fake them, please!) from your past customers or even experts in your field.
d) Make payments easy. PayPal and Google Checkout are easy-to-use third party payment processors.
e) Don't use cheap marketing tricks like "Last chance to buy...!" or "You can only buy it in the next 10 minutes! 9! 8!..." Your customers are not naive.
f) Finally, don't ever forget that you HAVE TO ADD A VALUE.

5. Non-Commercial Website
Even if you run a small blog about celebrity babies, dog breeds, auto repair etc. and don't do any of the above mentioned, you can still earn money from your site/blog.
The idea is to be yourself, write compelling content that people love to read and share with others. If you succeed, you might get offers where people ask you to write a column for their website, offer you a paying gig etc.
As long as you bring some value to others, you can always make money with your site, even if you have a website to share your opinion.