What is the fastest way to level up my speech skill?

Go to riften and go to the black briar shop speak to Ungrien and speak to him about maven black briar then after that persuade him to tell you the truth if about 10 mins you will have 70 speech then go to riverwood and speak to the man in the shop next to the forge and invest in his company then do two 24 hour time passes then go back in the shop and sell loads of items and u will have 10K gold

What I did was make a new character (Breton or Nord, since they are the only ones that get +5 to speech) and then I picked all the plants and killed a bunch of animals, combined with the stuff from Helgen Keep. I got a couple of level ups from selling the stuff to Lucan. Do this a lot whenever travelling and then you will make a lot of money and level up speech a lot. Also level up stamina when doing this, so you have a larger carrying capacity.

Try taking 20 cabbages, sell them and then buy them back. It costs very little because of the low item cost.

SPOILER, even larger glitch

Fastest way to increase speech is by geting something with fortify alchemy (eg ring), create fortify restoration potion and drink it, then unequip and reequip the ring and create another potion. Repeat until you have effect like +6544564% alchemy (just masching numbers, but ingame it looks similar) and create superstrong and super expensive potions. Sell just one and you have 100 speech (and in the process you got 100 alchemy) ps don't megaboost enchanting it can crash your game when you want to enchant with +much% enchanting

This exploit is game breaking, you can use it to make bows that oneshot anything (500+ damage), and other unreasonable bonuses. And then its even easier than playing on easy, so why bother. But its easy way how to get last few points of alchemy/speech, so I recomend not using it or using it ONLY for those level ups (and then use "normal" falmer helmet trick to make strong equip, but not so ridiculously strong).

I found it very effective to try and steal from guards, then persuade them to overlook it. They will let you go once. Every guard will let you go exactly once, the second time around that exact guard will not look the other way, but instead he will arrest you.

Does it increase my speech skill when I wear fortify speechcraft and haggling clothes and drink fortify haggling potions?

These are skill modifiers. They provide an increased speech skill while working, but do not raise your speech skill or provide skill experience.

How can I level up my speech skill? Does selling items and persuade people to tell the truth increase my speech skill?

You can persuade people, but the opportunities to do so are few and far between.

You can also find a speech trainer to convert gold directly into skill levels. This gets expensive above skill 50.

Instead, the fastest way is to interact with a merchant. Both buying and selling provide speech experience. The amount of gold determines this amount. Selling 5 items for 20 gold each or 1 item for 100 gold grant the same skill experience.

If you just buy and sell the same item back and forth to a merchant, you'll rack up a bunch of skill experience while only losing a portion of the item's value in the process. You could also combine this with other skills... Buy ingredients, craft a potion, sell it. Buy materials, make a weapon, enchant it, sell it. The more money that changes hands, the more speech skill you will gain.

The fastest way is to barter i.e sell stuff to merchants. Persuading people also increases your speech skill, but it is easier to increase it by selling items since finding people to "convince" is more time-consuming.

Good luck!