In general, it is permitted to borrow items that one needs on Shabbat. The Shulhan Aruch in Siman 307 states that there are certain Hebrew words that have a problematic connotation and may not be used on Shabbat out of concern that it will lead one to write. For example, one may not ask to borrow items using the Hebrew word "Hal'veni"- (lend me). It has the implication of a long-term loan which people generally record in writing, so that they don't forget. On the other hand, it is permitted to borrow using the word "Hashi'leni," which is also a term for borrowing, but implies a shorter term.
These nuances are not apparent in English. Therefore, the Poskim state that all terms of borrowing and lending are prohibited. One may borrow by using the terms, "Give me," or "Let me have it." For example, if someone needs a corkscrew on Shabbat, he can ask his friend for one by saying, "I need a corkscrew. Please give me one, and I'll give it back to you."
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It is prohibited to talk on Shabbat about doing an activity after Shabbat that would not be allowed to be performed on Shabbat. For example, one may not say that he is going to pick the tomatoes in his garden after Shabbat. On the other hand, it is permitted to talk about activities that plans to do after Shabbat, if those activities may be done on Shabbat. For example, one may say that he is going to check on his garden after Shabbat, because it is permitted to watch one's garden on Shabbat.
SUMMARY
One may borrow items needed for Shabbat, provided he does not use terms of borrowing or lending.
It is prohibited to talk about performing an activity after Shabbat that may not be performed on Shabbat.
