TODO: Remake for year 2022 lol
Though most people only see the end product, the process of making a TAS is just as important as the TAS itself. This page expresses various details.
Choose a game such that you would find making the TAS rewarding
Try to imagine what the final product will look like. If you don't know, do some research (explained below). You will need to find it rewarding, or else there's really no point in TASing.
We have a list of ideas, but don't follow that page blindly. You should choose for yourself.
Do your research
The first thing you should check for is if other users on this forum have made or tried a TAS of the game you want to TAS. Search the forum as well as this wiki, since someone could have made a submission on that game. If you know or suspect that the game you are TASing has an engine similar to another game that has already had a TAS submitted, check it out to see if particular tricks or glitches used in it are applicable to your game as well.
You should also check other resources, such as http://gamefaqs.com and http://youtube.com. Someone could have posted useful tricks or shown a gameplay video doing something you didn't think of.
Don't forget to check http://speeddemosarchive.com (including the forums), as someone could have made or tried to make a speedrun of that game.
It is important that you do the research. You do not want to lose out because of inferior knowledge. As a side note, rules do require that you beat all existing records, but this goes without saying.
Test the game
Before making a good run, you should test the game. This includes making a test run. You will definitely learn something as you test.
Test run does not mean half-assed run. The purpose of a test run is to gain information that would be very useful when making the good run. You can (and should, in a test run) use auto-fire rather than find the first frame of whatever, but you must stick to TASing in a way so that it looks convincing. Don't let up, or else everything will start to look bad and you won't learn anything. That being said, you don't have to TAS the whole game if you know that you can do it in the good run.
You should definitely focus on finding the best route for the run, if there are a lot of possible routes.
Use the best tools
There are tools in each emulator for a reason. Very often these tools help, if you know how to use them correctly. Memory search and Lua scripting are just a couple. You may not necessarily need them, but do know that they exist.
Find out how to make it better
Keep thinking about how to make it better. If you think of a possible trick, try it out. It may be surprising how often a simple idea becomes TAS reality.
For example, if fighting a boss in a Mega Man game, it may be as simple as having the boss do something different, or doing an attack combo, or something. The more variety, the more it entertains new ideas.
Shortly: Think outside the box.
Let others help
It is a good idea to report it to the forum and show WIPs. That way, others can give you feedback, perhaps useful information. Better to do it sooner than later.