The Medium skill is a central part of all the new content introduced to The Sims 4 in the Paranormal Pack. It will allow you to commune with the dead, summon spirits, and do all kinds of ghastly things. You can also use your powers for good by banishing ghosts and getting messages from the dead.
The first thing you will need to do is get a Seance Table. You can get a standalone séance table in the Build/Buy catalog for $333 or a full set of a table, chairs, and crystal ball for $648. The table is the important part, but you will also need a chair to sit at it, so make sure you at least have a spare chair if you cannot go all-in on the fancy-looking full set.
After that, all you need to do is start using the séance table, which in turn will start increasing your Medium level. Think of it as a case of practice makes perfect. There are some factors that will impact how quickly you can level up your Medium level, however.
You need to successfully complete that various rituals, so you will want to make sure your Sim is in a good mood when you are doing them. Items like Sacred Candles, available from the rewards store, will help with this.
There will be different actions you can take by using the table, and each one will increase your Medium level if you complete it successfully. You still make some progress if it goes wrong for any reason, but it won’t be optimal progress.
At Level 1 you can perform the “Sense Spiritual Volitivity”, “Perform Ceremony, and “Commune with the Departed” options. The first option will get you a small bump, but is an important step to take, while the last two getting a larger bump but cannot be performed as often. From there, it is just a matter of repeating your interactions until you break through to the next Medium level. Once you manage to unlock them all, and peak at Medium level 5, you will receive your Paranormal Investigator License from Guidry the friendly ghost, if you ask him for it.