Each free trade agreement sets the terms, so the answer will vary by FTA. In the case of NAFTA, the terms of withdrawal are dictated in Article 2205. Specifically:
Article 2205: Withdrawal
A Party may withdraw from this Agreement six months after it provides written notice of withdrawal to the other Parties. If a Party withdraws, the Agreement shall remain in force for the remaining Parties.
The 6 month written notification is fairly standard for most international agreements, free trade or otherwise.
Article 2205 also answers whether or not a country can force another out: No.
If one country were to leave NAFTA, the others would still have the agreement, at least nominally, but if that country were the U.S., Mexico and Canada would have a hard time making NAFTA worthwhile.
The U.S. could, in theory, agree to leave NAFTA at the same time as Canada, and then immediately resign an identical treaty with Canada, which would have the effect of kicking Mexico out. The realities of politics in both countries make such a course of action unlikely, as once the treaty is open for renegotiation, then interest groups in both countries would want to seek better terms than they got 20 years ago.