On Tumblr, although it is not possible to follow specific people, like on Twitter or Facebook, it is possible to follow their blog. You can find a person's blog by searching for their username, the name of the blog in question, the person's email address or related categories.
Steps
Method 1 of 2: Use the mobile app

Step 1. Open Tumblr
It's a dark blue icon with a white “t”. This will open your dashboard if you were previously logged into Tumblr.
If you were not signed in to Tumblr, enter your email address and password

Step 2. Select the magnifying glass icon
It is located at the bottom of the screen. This will open a search bar and your phone keypad will be displayed.

Step 3. Type the name of a blog
You can also enter a person's name or blog URL, as long as this information matches the content of the blog in question.
If you're not looking for a specific person, you can type in a keyword like “video games” (or something more specific like “dark souls 3 art”)

Step 4. Tap Search
This key is on your phone keypad. This will launch a Tumblr search for that blog, person, or keyword.

Step 5. Select More Tumblrs
This can be found at the bottom of the section Popular tumbles. This allows you to see all the results that redirect to blogs.

Step 6. Start following the blog that you were looking for
Choose Subscribe located in the top corner of the blog. From now on, posts from this blog will appear on your dashboard.
Method 2 of 2: Use a computer

Step 1. Open Tumblr
Go to Tumblr. This will open your Tumblr dashboard page if you were already logged in.
- If you were not logged in, click Log in, enter your email address and password, then choose Log in.

Step 2. Select your profile icon
It represents the silhouette of a person and is located at the top right of the dashboard. When clicked, a drop-down menu is displayed.

Step 3. Choose Subscriptions
You will find this near the beginning of the drop-down menu.

Step 4. Click on the Subscribe text bar
It is located in the center of the page, just below the header Suit # Tumblrs.
If you are not looking for a specific person, you can use the search bar at the top left of the page

Step 5. Type a blog name, URL, or email address
Be sure to enter the name or words exactly as they appear on the blog (or in the email address).
If you are using the general search bar, you can also type in a keyword (for example, "dogs") to search for blogs that match that topic

Step 6. Choose Subscribe
This option is to the right of the search bar titled Subscribe. You will then automatically become a subscriber to this blog.
- If you are using the search bar, press Enter and then click Subscribe next to the blog you want to follow.