1) The first sign of twins has got to be rapid weight gain, early on during your pregnancy. I am sure there is no need to mention that your uterus will expand quicker if you are pregnant with twins. I'll lump an faster increase in fundal height in with this point, because you might notice this before you actually step onto the scales. If it is not your first pregnancy, you are likely to grow quicker though.
2) More severe first trimester symptoms are another very common sign of twins or multiple pregnancies. Very heavy morning sickness, extreme fatigue, and dizziness can all indicate twin pregnancies. Mind you, you can still be carrying twins if you don't have excessive symptoms they are just more likely to be more noticeable in the first trimester.
3) Feeling fetal movement earlier is another possible sign of twins. If you are carrying twins, they are likely to be active and even interact with each other. If two babies are dancing all over your uterus, it is no wonder that you might be feeling them kick sooner than singleton mothers.
4) This last point is not something you can detect by yourself. If you have had a blood test that showed high protein levels, this is another indication of a possible twin pregnancy. OBs who get results like this will definitely order an ultrasound.