First, don't change everything at once. If you start adding fiber all at once, it can backfire: bloating, gas, and even more digestive issues. You need to increase it gradually over a week or two and drink plenty of water, because fiber doesn't work well without water. And don't get obsessed with laxatives right from the start; usually dietary changes will sort it out.
Fruits and vegetables are the basics: apples with skin, pears, bananas, berries, raw carrots, broccoli, spinach. Legumes like lentils, beans, and chickpeas have tons of fiber and protein. Whole grains are also your friends: oats, whole wheat bread, brown rice. A bowl of oatmeal for breakfast or a handful of almonds as a snack work great. Kiwi is particularly effective for a lot of people; flaxseed also works if you grind it and add it to yogurt or smoothies.
The key is consistency. Eat these things daily, not sporadically, because your body needs regularity to adapt. Drink plenty of water throughout the day, and if you don't see improvement in two or three weeks, then check with a doctor. Sometimes there are other causes behind constipation that aren't just lack of fiber.