If you have your own room or live alone in an apartment, make sure you aren't spending more time there than outside.
Bring baked goods or small gifts to your neighbors and introduce yourself to the neighborhood. This gives you a chance to meet the people around you, practice any language skills you're learning, and learn more about the culture of the country. It will also come in handy if you ever need help with anything. Learn from your neighbors. Find out how to be an ideal guest. Does the culture of this country require gifts when you are visiting? Should you take off your shoes? Watch and learn. Ask people to tell you about themselves and where to find the best groceries in town.
Smile at the clerks in the grocery store and visit the local markets often. They will be more likely to be friendly to you and patient of your rudimentary language skills if you are warm and friendly. It will also help you feel more welcome in town and less likely to miss home so much.
Accept invitations. Don't run home after work. If someone asks you over for dinner or out for a drink, take them up on it. You'll make friends and won't be sitting in your room wallowing in depression and self-pity because you miss your family.
When you start to make friends, invite people over for dinner or to celebrate your holidays. You can make your favorite American dishes for them and teach them about holidays they might not celebrate in the country.
Find an Internet cafe if you don't have Internet access in where you live, and write home every couple of weeks if possible. It will improve your outlook and curb homesickness.
Download Skype, a free program from the Internet, if you do have access to the Internet from your own computer as well as a microphone and web camera. That way, you can talk to and see friendly faces back home. You can video chat for free from your Skype account on your computer to their Skype account on their computer.
Write letters if you don't have Internet access, and send little mementos home. Tell family and friends to write you letters and send packages. Receiving mail in a foreign country from family is exciting, and will be something to look forward to if you're feeling lonely.
Take up jogging, bicycling or make time to go for a walk to get the blood flowing and make you feel better about yourself. It's also a good way to work off nervous energy.
Continue the pastimes you enjoyed in your home country. If you're a writer or you like to listen to music, make time to write or jam out to some tunes. Neglecting yourself and the things you like to do because everything is so new and scary might cause you to withdraw and become lonely and depressed.
Notice the hobbies of your new friends or neighbors, and ask them to teach you. Maybe they can teach you to make something unique to that country. If you have free time, learn to dance traditional dances, make jewelry or cook new recipes of the country.