Leveling up in Skyrim Special Edition is not as hard as it looks and fortunately there are ways to make the process shorter. However, there are certain facts that must be noted when a player wants to level up quickly. Firstly, specific enemies including the dragon will level up with the player so leveling up doesn't make it any easier to defeat it. Second, a player needs to focus on particular attributes to be able to improve their stat so a player needs to know what he wants to improve so he can focus on that attribute. And lastly, you need the mage stone active if you wish to level up your magic stats, choose the warrior stone if you wish to level up your combat and thief stone to improve your thief stats.
Leveling Up the Magic Stats. The first and easiest way to get an XP bonus for this stat is to sleep with your wife when you're married. However, if you're not married, use the Muffle spell as often as you can. If you need more Magicka, just wait for one hour and it will be refilled. There is another way if you already have the Equilibrium spell. Use the spell to do damage on yourself and set a healing spell on your other hand so you can do both casts again and again.
Leveling Up the Combat Stats. One of the quickest ways to level up a weapon is to complete the Dark Brotherhood questline so you can have Shadowmere with you. Since he is an invincible horse, you can do attacks on him using the weapon that you wish to level up. Now if it is armor that you wish to level up, just look for a guard tower or a giant and start doing punches while wearing the armor. You just need to do this continuously and your armor will surely level up.
Leveling Up Thief Stats. Improving the stat is pretty easy. Just look for a big crowd and sneak around them. Some people could notice you but to those that did not will give you XP for sneaking on them. If you're up for more challenge you can also do lockpicking or pickpocketing to as many as you can.