The best advice my dad (also a USAFA grad) gave me before I left: "The days are long, but the weeks are short."
Put yourself in the mindset of living meal to meal, ie "I'll just make it to breakfast" or "I just have to get to dinner." During basic, it can be very tough to keep going when you think "it's going to be like this for another __ days." Living in the moment, or meal to meal, will prevent you from getting overwhelmed with thoughts of what is still to come.
In 1st BCT, find a way to calm and "recenter" yourself when you are allowed to go back to your room. For me, this was washing my face. Usually, you'll return to your room after being physically trained, yelled at for your inability to follow simple instructions, and stressed to the max. You'll be frazzled, confused, down on yourself, and exhausted. Take a moment to separate yourself from the stress, calm down, and then put your "game face" back on.
Your classmates are everything; you will succeed and fail together. This is initially a tough one for many basic cadets, because to get into the academy you have to be very successful individually. During basic, the game changes. You will not only be responsible for your own appearance, knowledge, and military bearing, but also for your classmates and specifically, your roommate. For example, lets say you fall out for formation with a perfect uniform, but your roommate's nametag is on the wrong side of his shirt. He will be punished for wearing an incorrect uniform, and you will be punished for not checking him before you left.
You are not alone. Feeling alone is tough, especially during the first week of basic. You don't know anyone in your flight, you're tired, you can't do anything right, the cadre are constantly at you for minute things, and it's hard to see a light at the end of the tunnel. Just remember that 1000 of your classmates are going through the same thing, and feeling the same way you do. As basic goes on, you will find that the shared hardship bonds you to your flight-mates like nothing else can.