1. To suggest that some action be taken. I propose to move the meeting to next week. We propose to join forces and repel the invaders as a single, unified army!
2. To make a suggestion to someone. In this usage, a noun or pronoun is used between "propose" and "to" to specify what is being suggested. I suggested a slightly different way of wording the text to the boss, but he got really mad at me for it. They're proposing a lower price to us for the house seeing as there were so many issues with the plumbing.
3. To ask for someone's hand in marriage; to make a marriage proposal. I'm planning on proposing to Judy while we're in Paris. She proposed to me on my birthday.
propose something to someone
to suggest something to someone. I have an idea I would like to propose to you. Sam wanted to propose a new plan to Sarah.
propose to someone
to suggest marriage to someone, usually a male to a female. Guess who proposed to me last night? Do you think that Sam will propose to Mary?