If you are new to the baby-making game (or perhaps you are just curious), the short answer to "can you get pregnant right after your period" is YES! However, don't be alarmed - let me explain further. The answer for most people is generally not that black and white but it is possible.
You may be surprised to learn that your cycle actually begins on Day 1 of your period. Your period lasts anywhere from 3-10 days depending on your body. Most women average about 5 days but this will not be the same for everyone. Hopefully you are one of the lucky ones that has a short period!
Then in the middle of your cycle, you will release an egg (this is called ovulation) and there is a very short time frame for the sperm to actually reach the egg if you have intercourse. Once the egg has been released then the chance for fertilization goes down very rapidly. Generally, it is best to have sex a couple days before you ovulate. Sperm can survive several days inside your uterus and they better be there waiting for the moment the egg is released for optimum timing.
Once ovulation is complete then you have approximately 2 weeks until your period shows up again (or you may test positive on a pregnancy test). Again, this depends on the woman but this generally holds true.
Now, back to the original question...most everyone is taught in junior high health class that women ovulate around Day 14 of their cycle. This is AVERAGE and is also assumes the woman's cycle length is the AVERAGE of 28 days. Since this is an average that means there are many women who ovulate before Day 14 and many that ovulate after.
So if you are one of those women who tend to ovulate earlier (say Day 10 or 11) and your period lasts 5-7 days, then yes, it is possible to get pregnant right after your period if you have intercourse soon after your period ends! Although, you obviously won't know you are pregnant until it is time for your next cycle to start. That is because the hormones that are released once you become pregnant will not trigger a positive urine pregnancy test until is it almost time for your cycle to start over.
The moral of the story is that is it possible to become pregnant right after your period. The best way to know for sure when you will ovulate is to use ovulation test kits.
There are as many questions about How Do You Get Pregnant as there are women! Educate yourself even if you are not trying to get pregnant. That way there will be no surprises.