You can do the recipes that came with the Mr. Beer kits, but I would recommend first ignoring the kit directions. First, make sure everything is sanitized. Do a full boil for at least 10 minutes with the extract and all the water needed (forget about using water to cool the wort down, you can do that in a water bath of ice and water in your sink.) Rehydrate your yeast before pitching, don't sprinkle the dry yeast on top.
Next, keep you fermentation temperatures down in the mid to upper 60's and allow it to rise a few degrees during fermentation. Allow it to ferment for 10 to 14 days.
When bottling, make a sugar solution by dissolving the amount of sugar you need in a pint of water and boil for 5 to 10 minutes. Cool to room temperature and add to your LBK stirring in very gently and then allowing it to sit for at least an hour to allow the yeast to resettle, then bottle directly from the LBK.
You can also use one LBK as a bottling bucket for the other to get it off the yeast before mixing in the priming solution.
Once you have those done, or if you feel much more adventurous, look at some of the recipes on HBT and you can scale them to fit the size of the Mr. Beer kits. Chances are high that they will come out much better than the prepackaged Mr. Beer recipes.
^ Good advice here. To piggyback a little bit now that I'm home on my computer instead of my mobile:
Sanitation - this is key. When I got my Mr. Beer kit, I think it came with One Step and that was supposed to be for cleaning and sanitizing. It's really only a cleaner. Use something like Star San or Iodophor for sanitizing. If you use bleach, be aware that chlorine can cause off flavors in the beer even in unbelievably small amounts.
Water - Again, chlorine is something I am going to highlight. If you have any chlorine or chloramine in your water (basically any municipal water supply), you'll want to get it out. Campden tablets (Potassium Metabisulfite) work perfectly. The flavor you are trying to avoid is a nasty band-aid type flavor.
Yeast - you can use the yeast that comes with the kits, but frankly you can get better yeast very easily and it doesn't cost much at all. Check out US-05 for an easy to use dry yeast with a fairly neutral flavor profile. +1 on rehydrating, and also take a read through the
Dry Yeast FAQ for easy rehydrating instructions and other info related to dry yeast.
Temp control - You want to try and keep the fermentation temperature steady and near the lower end of the ideal range for the yeast you use. For most ale yeasts, that means starting fermentation in the low to mid 60's. At the very least, set the fermenter in a large tub of water that you can add ice to in order to maintain the temperature. Fermentation produces heat, so leaving it setting out a room temp could mean you are fermenting 10* higher than room temperature at the height of fermentation.
For bottling, you might also consider grabbing a cheap food-grade bucket from Lowe's and an autosiphon from a home brew shop ($10 maybe, probably less). Then you don't have to worry about stirring up any of the trub (sediment) when you add the sugar.
