The process of kneading your bread dough develops the gluten of your flour. This stretches your bread, allows it to trap the gases, hold in air bubbles, and double it's size. After you've added flour until the dough is soft and not excessively sticky, it is time to knead.
Hand Kneading - First, get comfortable. I find it easier to knead with arms out stretched and locked elbows so that I can use my body's weight to help with the kneading. A kitchen counter can be higher then you can comfortably knead, at least if you are short like me, so you may wish to move to a table. Rub some vegetable oil on the table and your hands. Now position your dough in front of you and push the heels of your hands into the dough. Fold the dough over itself, and repeat. (This sounds complicated when written down. You need to come over so I can "just do it"!) In a few minutes, the dough will begin to feel smooth and elastic. To test if the gluten is developed. Pull a golf ball size ball of dough between your hands. It should stretch without breaking. Kneading is something that will come by practice and experience. Start with a small amount of dough (pizza dough is perfect) With some experience and strengthening of your arm muscles, you can knead large batches of dough. Sometimes it is easier to divide a large amount of dough in half and work with them separately. Or call in some reinforcements! One lady said that she would divide her dough in small amounts for one loaf of bread each and call all her children into the kitchen to knead for a few minutes! Family togetherness while providing daily bread!
Machine Kneading - If your electric mixer is equipped with a dough hook, you can knead your dough in your machine. After adding your flour, turn your machine to medium speed. Usually you will knead for about 1/3 the time of hand kneading, about 5-7 minutes. Just stay close to your machine. Occasionally the dough will all go to one side of the bowl and cause your machine to "walk" off your counter! I caught my machine just as it was falling this week! You can check your gluten develop by stretching the dough, as mentioned above.
Bread Machine - I have no experience with bread machines but I understand that you can use them to mix and knead your bread even if you prefer to shape your dough and bake it in your oven instead of finishing it in your bread machine.