Welcome to ATP
Yes, good guess! Thin and puny and vine-like means they're not getting enough light. They grow long, skinny stems because they're 'reaching' for the light. As soon as the seedlings pop up, they need good bright light for at least 7 hours. Brand new seedlings can benefit from filtered light, such as you'd get through a sheer curtain on a sunny window. If you don't have a window that gives good light for that long, you might need to try a grow-light of some sort. You don't want them growing in too warm conditions either, so cool 65 to 75deg. and bright light is good.
When the weather's good, (above say 65deg.) you can set them outside for direct sunlight as soon as they have their second set of leaves. Be sure to bring them in at night, though. Keeping them moist but not over-watering is another challenge. Water every morning, and just wet the medium, don't spray the tiny plants or they could flop. Check the surface of the soil/medium later in the afternoon, and don't let them dry out. This is going to depend somewhat on the humidity of the air in your house. Mine don't dry out easily, but I am in Florida.
What kinds of seeds are you starting?
