How do you deal with enemy titans while you're not in a titan?
What is the best thing to do as a pilot with no access to your titan, when the other team is mostly in titans? Should I mostly be hiding and taking potshots? Should I be running for my life? Should I stand my ground and do as much damage as I can before I'm inevitably murdered?
Also, I've seen other players mount enemy titans to land some kind of special attack. How do you do that?
Mounting a titan (known as rodeo'ing) is pretty easy on paper. You just have to jump into the uppermost part of the titan and it automatically goes through the sequence of attacking the titan.
The first time you or an ally rodeo an enemy titan you will steal their battery. The battery grants the titan a shield and some hp. Once you steal the battery you can give it to any friendly titan to grant them that shield and give them some hp. Any time you rodeo after the battery is stolen, your pilot will drop a grenade into the empty battery socket dealing a good amount of damage to the titan. The real difficulty of rodeo'ing is getting high up enough to trigger it all while not being noticed.
As for what you can do beyond rodeo'ing it highly depends on your weapons. Energy weapons and explosives hurt titans a good amount, regular bullets barely do enough to even waste the time shooting at them. The best advice I can give is to stay high up and use your mobility to your advantage. titans are slow moving and can not chase pilots well. Titans can not jump (except the ones with the fly ability) so staying high makes it far easier for you to get to cover when a titan does notice you. If you have to staying indoors is also good but it makes it hard to harass the titans.
If there is a 1v1 titan fight where your opponent and a friendly are fighting then by all means join the fray. Pot shots do help (you can see the glowing red section, usually on the face, of a titan where your weapon will do the most damage), as well as grenades (especially the blinding one), and if you have one an anti-titan weapon (these are quite powerful).
Rodeo'ing a titan should be a low priority. Often you get run over on accident, and if you do make it on you tend to be a large target - especially considering the fact that if you pull a battery there is a bright green icon that you carry until dead or deposited.
If there is a large group of enemy titans, then running and hiding is a good approach. If you have a titan that has the nuclear eject option, then you can attempt to hide, drop your titan on one of their titans, and then allow the remaining ones to group up on yours only to nuke them all at once! This, however, is tactically very trying and in practice can end up in attempting to do too much.
All that said, if you were inclined to go solo a group of titans with just you (aka suicide) then make sure you choose a very quick approach vector. This should include several walls to jump on in order to "fly" in. Attempting to get their titans into a bottleneck area, as opposed to in the open, will help greatly. You can do this by baiting them with your primary weapon into following you. So, you get on the first titan (miracle) and are pulling the battery out. At this point the battle will start focusing on you, and more than likely another titan will scrape you off. Or the ordinance will kill you. If you somehow manage to grab one of the batteries off, and nothing kills you, then proceed to attempt to do the same thing to the same titan. Jump off, hover, the land back and pull another or drop in a grenade. If you can manage at this point to do that, and then get on an adjacent titan to pull a battery, you should have enough percent to drop your titan... directly on the titan you are rodeo'ing in our epic story line. All that is left is to battle the leftovers in your titan. Good luck! :D