Greetings and good luck with the brewing! I started about 20 years ago now. Brewed a few batches in the first 18 years, and then suddenly got the itch again and this site has been an enormous help in my learning. Here are a few tips that I've learned, specific to extract:
1. Sanitation - Most important consideration. I highly recommend StarSan for it's ease of use and many other aspects. But sanitation is not effective unless you've cleaned first. You have to get the crud out before sanitizing. Oxyclean is great. PBW is better, but you'll have to ask yourself if it's worth the price difference better. I generally just use Oxy. I think PBW has a surfactant the helps. Oxy is loads less money.
2. Do full boils if possible. As a beginner, you may not have a large kettle. I dont' think they usually come in the basic kits. Generally people start with what they have in the kitchen or use something cheap. If you have a kettle that is capable, boil the full 5 gallons, or as much as you can. If you can't boil the full wort volume, then consider Late Extract Additions
3. Late Extract Additions - is boiling 1/3 of your extract with as much water as you can boil, then adding the rest with 15 minutes or so remaining. This will help prevent the carmalization of the extract. It will make any hops additions prior to the extract addition more potent because the wort is going to be thinner. Probably nothing to worry about.
4. Use Distilled Water - this is my opinion, based on what I've read around here and elsewhere. The reasoning is that water can affect the flavor of your beer due to the minerals and salts that it contains (for some confusing reading check out the "Water reports" threads..) Consider that when extract is made, the water is removed, but the minerals and salts are left in the extract. When you add tap water, or spring water, you are adding even more minerals to your beer, and you don't know how much of what stuf is in the extract. It's generally considered better to remove all doubt and just brew with distilled.
5. Use fresh ingredients - this is obvious. I recommend any LHBS (Local Home Brew Supply) that you know has a fast turnover of product. Or, many of the reputable online suppliers are a great alternative (sometimes a better alternative). Austin Homebrew, Midwest, Northern Brewer, etc. Their recipes and kits are generally the best to be had, and you won't get crappy instructions that tell you you can drink your beer in 1.5 weeks.
6. Yeast Pitching Rate - use the proper amount of yeast. Generally a single packet of dry yeast is sufficient, but I often pitch two. When using liquid yeast it's best to create a starter, to build up the yeast count. Look up how to make a yeast starter. Not necessary for dry yeast. Also, either dry or liquid is fine. Basic recipes will often be done with dry yeast, while there are lots of styles that might require a liquid yeast.
7. Fermentation temps - one of the most critical considerations is the temperature at which the yeast will ferment the sugars into alcohol. Too low and the yeast will not ferment very fast, or perhaps not at all. Too high and the yeast will produce flavors and aromas that are usually considered flaws. Ales ferment a bit warmer, usually in the 62-70 range I think, while lagers will ferment much lower, at around just above freezing to high 50s. Check the yeast instructions, or look it up online to be sure. There are ways to maintain the temps when you don't have a fridge and temp controller. It's well worth paying attention to this when brewing. It's probably one of the best ways to help brew good tasting beer.
8. Chill your wort - After boiling, it's best to cool the wort as quickly as possible. Many people starting out will chill their wort in the boil kettle, but sticking it in the sink filled with icewater. This is certainly better than not doing it, but most people also soon purchase or buils an Immersion Chiller (IC), or Counterflow Chiller (CFC) to chill their wort even faster. You might also consider doing a "No-Chill" brew, which is essentially sealing you boiled wort in a plastic container that is air tight and letting it cool on it's own. Do a search is interested. There is some debate about it's merits, but IMO it seems to have proven itself as a completely acceptable alternative. Some actually prefer it.
9. Brew what you like. - When choosing a recipe to brew, make sure you are brewing a style that you will want to drink. Whether it's a Pale Ale, or Stout, there is no great joy in making a delicious beer that you will not even drink. If you are unsure of what each style tastes like, pick up a couple of them from the store and see what they are like. I think Ratebeer and Beer Advocate are a couple of sites that people post their opinions of different beers. You can look up a style and try to find it at the store.
10. Relax, Don't Worry, Have A Homebrew! - Charlie said it best, and it's still the most profound advice in all of homebrewing. Don't get too worked up over any one thing (except sanitation). Most of the things that can go wrong while brewing will not make your beer undrinkable (except infections). So if you ferment a bit high, no worries. Pitch too little yeast? Pour a glass of homebrew and think about that beer you are making, as it will probably be just fine.
At some point you will start trying to do every little thing the best you can. That is great, but at the same time, many of the things that affect your beer you will be good at and not even have to think about. You will probably want to purchase more equipment to help make you brewing faster and easier. But never worry. It's just beer, and it's probably going to be just fine.