The conditionnel présent corresponds to English "would", and it's built the same way as the futur simple — same stem, including all the same irregular stems — but with the imparfait endings (-ais, -ais, -ait, -ions, -iez, -aient) instead: je parlerais (I would speak), je serais (I would be), j'aurais (I would have).
Beyond hypotheticals, the conditionnel is also the standard way to soften a request or make it more polite: je voudrais un café (I would like a coffee) is noticeably more polite than je veux un café (I want a coffee), and pourriez-vous m'aider? (could you help me?) is softer than pouvez-vous m'aider?