Ask your friends and family. The best and safest way to find a travel partner is to ask your friends and family if any of them would be interested in going with you. At your next family gathering or dinner with your friends, let everyone know you are planning on taking a big trip and would love to have someone join you. Show them the brochures and inform them of the price. If none of them are interested, ask them if they know anyone who would be interested. This person will at least have been vetted through someone you know.
Check the travel websites. Skip out on scammers and potentially dangerous people you will find if you post on a site like Craig's List. Instead go to travel information website forums where people list their trip and seek out travel buddies interested in going. For example, the travel website Lonely Planet has a forum for those looking for travel companions.
Use a travel matching service. There are websites that will help match you with a travel companion. Like a dating service, you provide information about yourself and are then provided with a list of potential matches. Try a site like Travel Chums or Travbuddy. Some matching sites even cater to specific groups of people such as seniors or singles.