A first session of a campaign can be a very interesting thing. Few sessions have me as anxious in a campaign than the first session, because a solid first session can set the tone and pace for a game that will carry for a good, long while if not the entirety of the campaign. My personal anxiety over session 1 is helped by how awful I am at beginnings. Still, it always helps to be prepared.
Ideally Have A Session 0 or Equivalent
Ideally you want to have a session 0. However, that is not always possible. In a session 0 everyone can talk about their characters, what they want from the game - if anything specific - and otherwise discuss about the game itself. Rules questions can be brought up. Clarifying questions on setting and characters can come up. It is effectively the table getting on the same page about how the game will be run and what will go on.
Not having a session 0 doesn't mean that stuff shouldn't happen. You can e-mail and have private conversations to make sure people are on the same page. You can have people submit character sheets via PDF to you to review before the game begins. You can try to have those discussions I mentioned online via e-mail.
For my own game I e-mailed out some world and area primers, a map of the region we'll be starting in and a general map of the continent they're on. I also e-mailed out Monte Cook's 'Consent in Gaming' form to get an idea of hard and soft lines for everyone. All of this has helped me plan the first bit of game, and also communicate my expected tone and themes.
Try To Check Characters Before Game
Whenever possible try to check and approve characters before the game begins. If you only have some sheets, than go over those. I like doing this because I find it easier to go over any hitches or needed changes in private 1 on 1 with the person than at the table. The privacy works both ways too as the person can make a case without feeling like they've got all eyes on them or slowing the game down. And best of all, it allows for time to think and sleep on things if someone does make a good case for something.
Plan Some Time To Talk About The Game
For Session 1 you still want to plan some time to talk about the game. A last chance for questions on characters/setting/rules/etc before the game begins. This doesn't have to be super long, but it could turn into a lengthy discussion so be ready for that. Don't fret if it does. You're much better off hashing all this stuff out before the game begins than trying to figure it out on the fly during game. It's a whole ton easier to do maintenance on a plane's engine before take off than it is while the thing is flying.
Just Get Started - Somewhere. Anywhere.
If you're bad at beginnings it is important to remember that no one is going to care once you get things going. So just start. This is where tropes can really help out. There is a reason so many D&D games start in a tavern, and it is because it is an easy way to put everyone in the same room where they can meet and come together. Wherever you are starting, just get the ball rolling. Fumble with it. Roll with it, but get things moving. Momentum will smooth out those rough edges and get you going.
Give Time To Establish Characters
You don't have to do this right off the bat, but in the first session there should be time to establish everyone's character in some way. Whether this is through some quiet time before or after the ball really gets rolling is up to you. It doesn't have to be a long time either. The idea here isn't that everyone gets to know everyone perfectly. Just that they get introduced and we get a first impression or idea of the person.
Some Game Mechanics Related Challenges Are Always Good
Normally I'd peg this as "plan a combat" but not all RPGs are about combat as their central mechanic and I think that is awesome. However, whatever your game is going to feature for its primary mechanical crunch should come up in the first session. This is important for you, to establish how you will run this and see how the characters react. It is also important for the characters and players who need to see how they react, and how they play out.
Three Ways To Go
This is more for your initial outing and could go beyond session 1, but try to have 3 different ways the players could go. If you are doing a more set story, having a single clear path is fine but for more open campaigns giving the players a choice can let you see what they are more interested in.
Once You've Started
Once the game is going momentum will help carry things. There are always start and stop points, but a game in motion tends to stay in motion so be prepared to just roll with that. Remember to have fun. If you're having fun, the game will be more fun for the players too.