The gateway to Colombia's Amazon rainforest is from Leticia, and the nearby small village of Puerto Narino. It's the ideal spot for rainforest tours, and it's perfectly safe - a long way from Colombia's trouble spots.
You'll need to catch a flight to Leticia - it's a very long journey by boat. Puerto Narino is a more relaxing and Amazon-esque type place to stay though. To travel onwards, it's easy to head into either Peru or Brazil.
Colombia's amazon rainforest:
River life near Puerto Narino in Colombia's Amazon.