When you are doing the arena and are about to fight the Grand Champion, do his side quest first so that he does not try during the fight. When you are about to actually fight him, go into game options and set the difficulty to "Very Hard". This give everyone you fight more health. When you are attacking the Grand Champion, get a lot more free hits in without worrying about him trying to fight back. This works even better if you are using a very weak weapon. It is not about how much damage you do that increases your levels, but how much you attack.
A major skill of Sneak and either Destruction or Alteration are required. If your skills are Sneak and Destruction, go to the Arcane University and go to the place to make spells. Make a Drain Health spell and make sure that it is set to "Self"and it only uses 1 Magicka. Then, go upstairs in Sneak mode and just run into the wall without stopping. Activate magic repeatedly. You will soon quickly gain levels. Note: When you activate the magic it will seem as if it is hurting you, but it is not. If your skills are Sneak and Alteration, go into a room with a container (for example, cupboard, drawers, etc.). Run into the container in Sneak mode and use a "open very easy lock"repeatedly on the container.
Make a Dark Elf with the birthsign Warrior and create a class with the following attributes: Athletics, Acrobatics, Blade, Block, Blunt, Heavy Armor, and Marksman. Next, complete the arena to get leveled up. Then, get a horse and find the lady in Kvatch. Note: You may have to shut the Oblivion Gate. Once on your horse, speak to the Orc woman at Kvatch and sell your most expensive equipped weapon until you have 55,000 gold. Then, join the Fighters Guild and complete your first mission. Go directly south of Imperial City and find a bridge. Cross the bridge to find a place called Vindisel. Kill a lady named Umbra and take her armor, shield, and blade. Next, go to Imperial City and mess with the guards. Every now and then, when you are about to die, run from Imperial City before the guards kill you or pay the fine using the gold from Kvatch. After you level up, go to any Fighters Guild and train your major skills. Then, attack the Imperial Guards and repeat.
For easy experience in Leyawiin (Blade, Blunt, Hand to Hand, Destruction, Marksman and Sneak), go to Leyawiin find Rosentia Gallenus' House. She has four Scamps. Kill them and more will respawn. Sneak attack with a blade, mace, or hand to hand. Then, use a bow and cast fire. Note: If you use your bow, the arrows are hard to get back. Note: If you finish the quest you cannot do this anymore.
Go to Cloud Ruler Temple northwest of Bruma and walk up the big stairs. You will see two Blades sparing. Stand near them for a minute and your Blade and Block skills will increase by 2. Note: This can only be done once.
Use one of the "Easy money" hints and get at least 500,000 gold. Then, find a place (taverns recommended) with two trainers who train in any two of your major skills. Train with one of them until you cannot do so anymore, then train with the second one until you cannot anymore. By now you should get the level up icon. Go to sleep and level up. Repeat the process until you reach maximum level or max out the two skills.
You must have Conjuration as a major skill and also need Blade, Blunt or Marksman. Summon a monster, such as a Scamp or Skeleton, and kill it with your weapon or shoot it with arrows. Repeat this for a couple minutes and you will get the message to level up. This may take longer if you already are at a higher level.