Q: I rush to find a level 9+ planet and I colonise it. I then lose what little profit I was making. Am I doing the wrong thing here?
If you look at the initial colony tile you'll notice that it provides research output and that it costs maintenance. All research output is funded in a proportion according to the percentage you set on your taxes screen.
So as you add colonies yo your empire, you will be funding more research and paying more maintenance. To start off with, each colony's tax income will not cover its expense so you may have to run at a loss until the population (and hence tax income) increases.
Q: On my new colony I buy outright a factory. Is this the right thing to do? I don't seem to be seeing any benefit. In fact, Im a little fuzzy on the benefits of factories in general...
Factories increase your manufacturing capability on a planet. You'll be able to build ships and buildings faster, again according to what funding has been set. If you're not planning on building anything (even just scout ships would do for finding more planets to colonise) then the factory is just costing maintenance, but if you're not producing anything then your funding for that planet is not used.
Q: I tend to buy another factory or 2 on earth as well. Is this sensible?
You're likely going to need to produce more colony ships there so you can argue that it's worth it. However, the quicker you build colony ships and settle colonies, the quicker you will find yourself going into the red.
Bear in mind that if you're playing on a larger galaxy, sending all your colony ships from Earth may take a number of turns. You'll want to to start building and sending them from some of the planets which are starting to grow in population.
Q: I send the mining ship I start with to a nearby asteroid field and it does its thing. Im not really sure what benefit this is giving?
Asteroid mines send raw materials to a nearby colony, increasing its manufacturing capability. The mines can be upgraded later on for greater output. The output can be redirected, but the further away the target colony is, the less materials will get through and the lower the bonus to the colony.
Q: Is there good way to start raking in some big bucks that Im missing? I don't have any trade routes or anything yet with other powers.
Your survey ship can occasionally yield money from anomalies. other than that, you want to let your population grow, and keeping the approval rate on a colony in the green (or if not green, then at least yellow). There are also buildings which increase Economy on a planet, these will improve your tax income, but bear in mind that these are only worth building once the population is a bit higher (let's say over 2 million) due to the maintenance costs. So make sure you have a couple of those on Earth - it already has a high population.
Q: Should I be building starbases early? Should I have one near earth?
An economy starbase, with the right modules, could improve your production and research on Earth. Unfortunately, starbases cost money to maintain - 5bc per turn. So it may not be worth it at the moment.
A mining starbase on a green resource improves the economy of your entire empire so it may be worth the cost. A yellow resource similarly improves morale empire-wide, which means population will grow faster or you can raise taxes a bit more.