I’ll add pictures soon, but here is the text. This assumes you bought a nucleus colony and have already placed it in a hive.
Once you have transported your colony home and set it up. Go ahead and open the entrance to a small opening (about an inch or two). You will probably be able to leave the entrance this small till the honey flow season of the next year. Keeping a small entrance on colonies through the summer and fall prevents other bees from robbing out the honey stores.
You should have already decided what your “overwintering configuration” will be. This is, how many, and what size boxes, your colony be for the winter. If your new colony is from a nucleus colony (5 or less frames of comb), or package bees, AND you will only be adding foundation frames to the box, I recommend you do NOT try and overwinter the colony in a “double deep” hive, and instead use a single deep plus one shallow or medium box. If you are already confused, keep reading, this is where the pictures will come in handy. I keep most of my colonies in a deep size box plus one medium size (or Illinois) box. However, I recommend using the smaller ‘shallow’ instead of the ‘medium’ to reduce back strain lifting the box. I do not recommend trying to start a new colony in 2 deep size boxes, if you are using foundation, because it is simply too much comb to expect a colony in Tennessee to be able to build through the Summer and Fall. Our honey flows (when bees really like to build combs) are early and short. You are highly unlikely to obtain bees before the honey flow starts in Tennessee to be able to take full advantage of the natural flow for your new colony to build combs. You will have to feed them through the summer and artificially get them to build new combs regardless of how you start your new colony (nucs or packages).
Which brings me to feeding: The same day (or at the latest the next day) that you setup your new colony at its new location, you need to feed it. I mix half sugar and half water to make a syrup for the colonies. The easiest way to do this is to figure 5 pounds of sugar makes 1 gallon of syrup. So, if you have a 1 gallon bucket, put 5 pounds of sugar in it, fill with water, then mix. Heated water is not necessary, but speeds the process. You will need to feed the colony continuously until every single frame in your ‘overwintering configuration’ is built with combs. It is possible you will feed this colony from the day you pick it up till it gets too cold to feed. However, it might not take that much. Sugar water will spoil. You don’t want to feed more than the bees can consume in 2 weeks. Especially in the summer, after 2 weeks, it will start to ferment and turn to alcohol, which your bees will consume, but it won’t be good for keeping them to the task at hand, which is to build up a big strong colony to overwinter. I recommend feeding 1 gallon to start then you can raise that to 1.5 gallons if they are consuming it all within 2 weeks. So, you will need to check the feeder every 2 weeks, if you have a 1.5 gallon feeder, which is the size I sell and use. When you check the feeder, also check how many frames have been built with combs. Once all but the outside combs in the bottom box have been drawn out with comb, you can add a second box. Since I recommend starting with a 5 frame deep nuc in a 10 frame box with a frame feeder (which takes the space of 2 frames), then you will be adding a second box pretty soon, or as soon as they build out their first comb. During the Summer in the Tennessee Valley (which starts about late June as far as the bees are concerned) the honey flow is over and nothing much is flowering. Its real important to feed the bees through this. The honey flow (or nectar flow, when plants produce nectar) picks up again when the goldenrod and asters start blooming in late summer / early fall. Continuing to feed them during the goldenrod bloom help them take full advantage of the natural nectar flow. They can tank up on sugar, go out and forage, and bring in a good crop to overwinter on. They need at least a full medium or shallow box of honey to make it through winter plus a little more. This will be the second box you put on your hive, and you want it completely full of honey (or syrup) and some more down below in the deep. A word of caution though. Always check the hive before feeding to make sure you are not over feeding. Overfeeding can result in a colony where the queen has no place to lay eggs because everything is full. You have to check and see how frequent to add more food.
Mite Treatments: The #1 problem, difficulty, and challenge with keeping bees is the varroa mite, which is a parasite that exists in every honey bee colony in the world (for all practical discussion), including yours no matter where you got it. The varroa mite is a parasite that feeds on the blood of the bees and transfers viruses and bacteria, which causes secondary infections. The majority of colonies in the USA will not survive 1 year without at least one mite treatment, if not more. However, some do survive without any mite treatments. Although I actively select for mite resistance in my honey bee breeding program, even the USDA professionals have not been able to develop a honey bee that is %100 resistant to the varroa mite. Most colonies die within a year without being treated with a pesticide designed to kill the varroa mite. So what to do? The question is not easy to answer no matter what your philosophy is. If you are someone that is happy to use pesticides in agriculture anytime you need, the answer is still very complex because most of the synthetic miticides are no longer effective. There are several organic controls that are very effective, however many conditions influence their effectiveness. I use and recommend either a thymol based product (Apigurad or Aplilife-Var) or a Formic Acid based product (Mite-Away). The difficulty for the new beekeeper with these treatments must be considered. First of all, they are hard on the bees. They reduce brood rearing in the colony and these organic treatments will kill small colonies outright. The reduced brood rearing will reduce the amount of combs they can build in their first year. I therefore recommend Apigaurd or Apilife-Var for the new colony because it is easier to regulate the dose of the mite treatment. You can cut it in half to treat the smaller colonies. The organics are also temperature dependent, which means you can’t wait till late November to treat for mites, because it will not work then. A full treatment of Apigaurd takes 4 weeks, so the temperature has to be warm for some time, but not too warm otherwise it will fume off too quick and possibly kill some of the brood. The organic treatments are essentially volatile, organic chemicals that kill mites but bees can tolerate more of these organic chemicals than the mites can. The formic acid product (Miteaway) is USDA Organic approved while the Thymol products (Apiguard and Apilife-Var) are approved in the European Union for Organic agriculture. The new colony should be of full size of the overwintering configuring before using these products, but if its too cold they won’t work. If they are too small, you can use half of the recommended dose. Hopeguard II is a new product that has been shown to be effective when little brood is in the colony (late fall).
Assuming you did all the above, and the colony responded well and is strong for overwintering, then you need to stop feeding liquid syrup after the first hard frost. If they need more food after that point, you will need to build a 1-2 inch spacer that goes on the top box where you can put solid food, usually hard candy or dry sugar. You can mix small amounts of water with dry sugar to make a paste, spread that on newspaper, and place it on the top bars which makes a pretty decent winter feed for colonies. Then, assuming they get through to spring, you might consider feeding them some liquid syrup in very early spring (late February in the East Tennessee Valley) and a mite treatment might be beneficial too, but many Tennessee beekeepers skip a spring mite treatment. After that, you can finally make some honey as the honey flow ramps up in mid-late March. April and May is the main honey flow in the valley, and you can make a decent amount of honey on overwintered colonies during this time, even if your honey supers have only foundation in the additional boxes to store the honey on. But, the colony will need to be large and booming with bees in at least 1 deep and a shallow box by early March to do much of anything with the honey flow. This is why you usdually don’t make honey on a colony you bought in the same year, in our area. The boxes for honey production go on top of your overwintering configuration. I always use, and recommend, a queen excluder between your overwintering hive and the honey supers. It takes a healthy, overwintered, strong colony to make honey in East Tennessee where we have a very early, strong, but short honey flow. The same is true for the higher elevations of Tennessee too, unless sourwood trees produce (an increasingly rare event) in the higher elevations. In that case, a weaker honey flow can last well through July in those areas and additional honey can be obtained in supers with drawn comb, but not usually in boxes with foundation.