How do I get Ordnance?

I have noticed that I sometimes get access to an "Ordnance Drop" similar to killstreak rewards in the Call of Duty series. I know that I am getting it for doing things, but I'd like to know how many of those things I need to do in order to get a drop. Also, is ordnance available in all game types? If not, in which is it available?

Personal Ordnance drops are obtained in Infinity Slayer and Big Team Infinity Slayer.

As 343 explains it:

As you earn medals, you fill up your ordnance meter. When that meter is full, you earn a reward drop for yourself from the Infinity. The reward comes in the form of three randomized power weapons, grenades, or powerups (two of the former, one of the latter). You can then choose which one you want, and the Infinity will drop the ordnance (if you’re inside, it will teleport in). You won’t get the highest tier power weapons (e.g., rockets) in personal ordnance, but everything you do get is powerfully awesome. And awesomely powerful. And everything in between.

The key part being "As you earn medals". Therefore the ordnance meter fills faster for doing more 'stylized' kills, such as Multi Kills, Assassinations, Retributions, Reload This, and the many more medals.

For an example:
If you throw a plasma grenade that sticks to an opponent who was reloading, then quickly assassinate another opponent, all while being shot at and then your team-mate kills the opponent shooting at you, that would net you 5 medals (Plasma Kill, Reload This, Assassination, Double Kill, Distraction) and significantly increase your ordnance meter.

Also a note from my own experience, you cannot receive an ordnance drop while in a vehicle. The meter still increases for what you do in said vehicle, but it will not show you how full the meter is nor will it inform you if it is full until you jump out of the vehicle, or you die. If you happen to die in the vehicle, or whenever you achieve an ordnance drop, you will retain the earned drop and be able to call it in when you next spawn.

Check out tombull89's answer below if you want to see point totals required for each drop.

As far as I can tell, you get ordnance drops from getting a certain number of points. So, when you get a message on the screen that says that you get points, the ordnance drop.

Ordnance drops are not available in all game types. The only game types (or at least playlists) that you can get ordnance drop in are Infinity Slayer and Big Team Infinity Slayer.