You can make money posting on Tumblr, but it takes a great deal of success as a blogger to generate enough interest in your page to make it profitable. You could use Tumblr to drive people to your website to purchase products from you, you could sell ad space on your blog, or you could use affiliate programs to capture a percentage of sales made after people visit your blog.
Whether you're looking at selling ad space, using affiliate links or just selling things on your own, your main way of generating money through Tumblr is via a lot of people visiting your blog. If you only have a few hits on your blog each day, you won't be very appealing to advertisers and you won't have many people buying things through your site. Look for ways to build up the traffic on your blog, generate high quality content that's consistent and connect with your audience. It can take time to build up a following that's worth advertising to. Don't rush it, if you don't have the numbers. Think about a thousand hits a month as about the minimum for starting to make money with your Tumblr blog.
Companies like Google buy and sell ad space. They will sell ads to their customers based on the number of people that might see or click on the ad. When people see an ad it's called an "impression." If you have enough people visiting your site you might be able to work with Google, through its Adsense program, to display ads on your blog. They will pay you based on either impressions or clicks; the more people who look at your site, the more money you're able to make. However, an ad-heavy site can backfire on you by driving people away, so don't oversaturate your blog with ads and do your best to keep them in line with your topic.
Some companies, like Amazon, will allow you to help them sell products as an affiliate. You become the gateway that people use to access the products and, in exchange, you get a percentage of the purchase price. You need to use special affiliate links from your site so the company knows that they should pay you for the purchases. This is a good idea if your blog does product reviews. For example, if you review kitchen products, you can post links to products that you like and earn a commission if people purchase anything through the link. It's considered to be good form on the Internet to disclose the fact that you're using affiliate links, so don't try to trick your readers.
If you have a product or service that you can sell, your Tumblr blog can serve as a great marketing platform. Find something that your customers will enjoy and offer it to them through your blog. For example, if you're a presentation designer, you might blog about public speaking and then have links on your Tumblr blog to your website, where people can hire you to do presentation work.