Surprisingly there is no official research on this but it is commonly accepted that the missionary position is among the best for conceiving. However, any positions that allow deep penetration (such as on all fours or lying down spooning) are theoretically best as sperm is placed right by the cervix and so doesn't have too far to travel on its own!
Its also generally accepted that upright positions such as girl on top or standing up aren't as effective. Some recommended avoiding lubricants as these can impair the movement of sperm or affect the hostility of the cervical fluid.
Some believe that lying with your hips raised up on a pillow, or legs in the air, for 20 minutes to half an hour after sex increases your chances of conceiving by giving gravity a helping hand. Again, whether this works or not is an unknown but some swear by it. Obviously you should avoid doing this if you have been recommended to do so by your doctor for medical reasons.
While following this advice is all well and good, the best way to increase your chances of becoming pregnant is to have regular sex throughout your cycle (2-3 time a week) with more around your most fertile time - using fertility charting methods will help you to find out when this is. Most of all its important to just relax and have fun - making sex mechanical and just for the purpose of having a baby doesn't do anyone any good and will just end up making you stressed. Try to remember that trying for a baby is meant to be the fun part!