Hi there.
This tutorial will take you through tellraw, which is a very complicated command. It is a raw JSON command, and we will probably get confused at some point. BUT, lets get on. Stick with me even when it is tough.

---

1) Using /tellraw

Tellraw is a command for command blocks. Do /give <Name> 137 or /give <name> Minecraft:Command_Block as the item id numbers will stop working in 1.8. Note that /tellraw will normally only work on singleplayer (or it doesn't work on my server anyways...).

---

2) The Simple Command (Base Command)

Well, you kinda already know /tellraw is your base command. But, this is the simple start (ALL /tellraw commands require this at the beginning):
/tellraw @a

---

3) Lets add some text...

Time to add text! Here is our work:
/tellraw @a {text:"Notch joined the game"}
Yes, you guessed it. We will be making a realistic Notch join message. Feel free to change this text to whatever you like, but all of my examples shall stem from this.

---

4) That realistic colour!

So, we will have to edit our code so far for this...
tellraw @a {"text":"","extra":[{"text":"Notch joined the game","color":"yellow"}]}
Yes, this is alot more complicated. I understand if you feel like copy and pasting this, so go for it! But, now, I will explain:
tellraw: Command
@a: Everyone online
"text": The Text Variable
"Notch joined the game": The Text
"color": The Color Variable
"yellow": The Color

---

5) Ok, now we have finished the simple stuff, lets underline it.

Now, we need to make the text underlined so it looks... cool.
We will need to, inside or brackets but at the end, add a comma and then "underlined". This is a boolean variable: It only can return true or false. We will set it to true, so we will add a colon and then, in speech marks, enter true. Ok, lets see if you have got it right:
tellraw @a {"text":"","extra":[{"text":"Notch joined the game","color":"yellow","underlined":"true"}]}

---

6) Bored. Lets make this... awesome:

Lets add a hover effect, or, in better terms: event. Take note on what we do here, as it will matter for the next part. I will give you our syntax and you can copy it and then I will show you what it does:
tellraw @a {"text":"","extra":[{"text":"Notch joined the game","color":"yellow","underlined":"true","hoverEvent":{"action":"show_text","value":"Is this fake or true!?"}}]}
Ok, lets explain:
"hoverEvent": The Variable. It is always in 'Camel Case'; the first word is lowercase and then all words start with a cap.
{"action":"show_text": What we will be doing.
,"value": Setting it's variable
"Is this fake or true!?: The hoverEvent text.

---

7) I'm still... alive. Now, lets make this amazing!

Our current syntax is above. We will now add a clickEvent to this. We will put the clickevent before the hoverevent. We will use the same rules. Try to figure it out!
Ok, here's the syntax:
tellraw @a {"text":"","extra":[{"text":"Notch joined the game","color":"yellow","underlined":"true","clickEvent":{"action":"run_command","value":"/say Yep, fake."},"hoverEvent":{"action":"show_text","value":"Is this fake or true!?"}}]}

Yes, we have to use a command in the clickEvent. Therefore, we can do many commands: We could use /tellraw or even /toggledownfall. Awesome, eh.

---

8) Congratulations!

Well done, you are now a /tellraw master. Feel free to take this further and ask me questions if needed. Feel free to subscribe to me if this helped you lots.