Ranked Mode unlocks when you reach profile level 15 and you own 14 Champions (free rotation characters do not count!).
Profile exp is earned by winning matches, just as character exp is. There's an Achievement tied to unlocking Ranked Mode (Here Comes a New Challenger) so when you get that Achievement you're on the right track.
This is a longer read than most guides but I wanted to ensure I explained things clearly enough.
All ranked matches are Siege so make sure you know what you're doing. Another suggestion is to know as many characters as possible because of how the game is organized:
When the lobby is full the player at the top of each team's list picks two characters to ban. This character cannot be used by anyone and in almost every match I've played it's been Moji and a healer of some kind (pre Open Beta Update 68). Also any new characters are auto-banned by the devs for 2 weeks.
Afterwards players get to pick, one by one, which character they want to use.
Once a character is selected that's it; no duplicate characters allowed. After everyone selects their character the match plays as normal.
As you play you will level up your characters as you would in casual matches so you could tie this Achievement in with getting characters to level 30 if you wish.
How Ranks Work - Qualifying
There are a total of 8 tiers: Qualifying, Bronze, Silver, Gold, Platinum, Diamond, Master, and Grandmaster. Qualifying is the default and is 10 matches long. When you complete those 10 matches you'll be placed on a higher tier.
Since you need to play 10 matches to earn a position you'd think you're being judged on skill, right? No. You're based on your wins vs loss ratio.
You can be the best player on the team, getting 30 kills, 2 deaths, and 18 assists every game and still be put on bronze tier because the rest of your team were wearing their pants on their heads claiming they were the Queen of Finland for 10 matches.
To summarize, this is about luck more than skill. Let the skill shine AFTER you're placed somewhere. Don't throw every match, obviously, but don't rip out your hair if you end up lower than you think you should be.
How Ranks Work - Bronze+
This can be the starting point of the problem for some and the saving grace of others.
Depending on how your Qualifiers went you may be really high, really low, or somewhere in the middle. Either way it's not too bad of a grind but it's still a grind to be sure.
On top of every tier (Bronze, Silver, etc) is a division
These divisions range from 1 to 5 (5 being the lowest division and 1 being the highest) and are what separates everything and is why it's such a grindy Achievement.
Let's say you made it to Gold tier, Division 3. You would need to earn 100 Triumph Points (TP) to ascend to Gold tier, Division 2. Then another 100 for Division 1. Then another 100 to reach Platinum tier, Division 5.
Basically you need to keep playing matches and earning TP to make any progress and every 100 TP in one division will move you on to the next. This is pretty forgiving compared to other games like Halo or CoD but it's still a pain.
While in Bronze, Silver, Gold and Platinum tiers, players may queue together in groups of up to 5 so use that to your advantage for gold and exp boosts as well as making the overall experience more fun. Diamond, Master and Grandmaster tiers may queue together in groups of up to 2 which still yields the bonus rewards.
Diamond Players may queue with Platinum tier players and Master and Grandmaster tiers have no divisions.
Players in Gold tier or higher who lose matches or remain absent from Ranked for too long will lose TP, and eventually will be demoted to the previous division/tier. The decay stops at Gold 5 so you can be at Gold 5 for two years and never drop below that level. Keep this in mind when you're trying to get Master level.