The simplest way to accelerate WordPress is usually to take advantage of caching. If you have a good hosting service, then it is included automatically with it. However, caching will not improve pure performance, the requests in the admin or the plugins related operations (such as bulk actions, scans, etc). Here is a checklist to improve WordPress performance.
Recent version of PHP
If your server is not using PHP 7 yet, ask for it. That will improve the performance drastically.
Restrict the number of plugins
The plugins installed on your WordPress has the biggest performance impact. Sometimes, even the plugins supposed to make your WordPress faster make it… slower. Use the minimum number of plugins possible, and don’t use a plugin which has too many features or options (except if you are using all of them).
Optimize the database
Delete revisions. Delete drafts. Run Media Cleaner.
Before cleaning your WordPress, make sure you have a backup for it. I recommend you BlogVault if you don’t have any yet.
Use the plugin WP Maintenance Mode to enable the maintenance mode. This will serve a static page to everyone, except administrators.
Run the plugin WP Clean Up and delete all the drafts – Check if there is any draft that is not an RSS imported post (categorized as ‘imported-photo’).
Clean Media Cleaner
Run the plugin Media Cleaner to locate and erase the orphan files, broken media, and files you do not need.
Disable Maintenance Mode
Disable the maintenance mode.
Test your WordPress install
Test everything in incognito mode or in a new browser (so nothing is cached). Double test everything with another computer.