To install WordPress you're system will require:
PHP 5.2.4 or Higher version, Recommendation: 5.6 or higher
MySQL 5.0 or Higher version, Recommendation: 5.6 or higher
Guide for a manual installation:
Step 1: First download WordPress from their official website: https://wordpress.org/download/, if you have not already.
Step 2: Upload the file you just downloaded to the public_html folder of your account by the use of File Manager in cPanel.
Step 3: Now, extract the zip file.
Note: By default the files reside in a sub-folder of the public_html one, if you wish to the installation of the application directly on your domain, you should move the file one folder back. To move files, open the folder and mark Select All button, then click Move File. Now your file is moved back to the folder.
Step 4: Go to cPanel > MySQL Database Wizard to create a database which will be used by the application. (It's recommended to write down the name of database, username, and password, which will be required during the installation.
Step 5: In the browser, open your domain where you will get the start page for the installation wizard. Select your preferred language for your application here.
Step 6: Just click on the Let's go button on the screen.
Step 7: On the next screen, will be required to do database settings for your application.
Step 8: Now, you need to click the Run button, and will be further guided by the instruction to install.
Step 9: This step requires you to apply the website settings.
Now, you've successfully installed your WordPress application.