For your first brew day, the best thing to do is not get too hung up on anything and make it through to the end. You're going to make mistakes. You're going to think of ways you could have made the session smoother. You're going to have ideas you want to implement next time.
That said, the things that I think are most important to focus on initially are: sanitation, pitch rate, fermentation temp, and patience.
You need to clean everything, and also
sanitize everything that will touch your wort after the boil. PBW or Oxiclean are pretty standard for cleaning, and StarSan or Iodophor are used by many for sanitizing.
For an ale, you probably want to target a pitch rate of .75 million cells per ml per degree plato - easiest way to figure that part out is to consult a pitch rate calc like
Mr. Malty. If you are using dry yeast, you should take note that pitching it without rehydrating can kill up to 50% of the yeast cells and you may want to consider pitching additional yeast to make up for that. Some people don't rehydrate, and don't pitch additional cells, and that is fine - the yeast will reproduce to the right size colony and make beer either way, but it doesn't make sense to me to kill half of the population before you even get started.
Yeast will make the best tasting beer when you help control temperatures to the lower end of the yeast's ideal range. For most ale yeasts, that is in the low-to-mid 60's. If you have a temperature controller, you can hook that up to a fridge. If not, you can place your fermentor into a rubbermaid tote full of water and use frozen 2L bottles to control the temp - look up "swamp cooler" on here and you'll see what I mean. The beer temperature is what you want to keep track of and control, not the ambient temperature. Fermentation is exothermic, so the beer will be warmer than the ambient temp, especially during the most active part of fermentation.
Patience... If you've done everything else right, your beer will need 7-10 days to finish fermenting and clean up fermentation byproducts. Many people leave their beer in the primary fermentor for 2-3 weeks (some longer) before bottling or kegging. Use a hydrometer to know when it is done - two readings taken over a 3 day span that are identical means your beer is done. If you are bottling, the beer will need around 3 weeks at 70F to fully carbonate. Then you can move a bottle to the fridge to cool and test to make sure it's ready. If so, toss a few more in the fridge for a few days to cool and let any chill haze form and settle out - you'll have clear, well carbonated beer as a reward for your patience.
