How do you say "there aren't people I can talk to"? 没有对他们可以说话的人？
"There aren't people I can talk to"

The translation varies, depending on what word is used to translate "talk to".


"说话", to get into a conversation


  找不到说得上话的人。

"倾诉", to pour out one's feelings


  找不到可以倾诉的人／对象。


or simply


  找不到倾诉（的）对象。



With "倾诉对象", the sentence is starting to become idiomatic. Other variants are also possible. For example, you can replace "找不到" with "没有". If the context permits, you can also say "没有人可以／愿意倾听／聆听我的倾诉". This last sentence is closer to "Nobody could/would become my listener".

The key here is that you need to find a word that conveys the meaning of "talk to" instead of just "talk". In other words, it should emphasize the action on the subject's part. Otherwise the sentence will just become awkward because you need to make up for the missed meaning. This is why dictionary translations of "talk" like "交谈" and "谈话" will get you nowhere---these words can only mean "talk with", which give equal weights to both parties involved in talking. Structurally this is similar to the deletion of preposition mentioned by Joe. But I think that this is more absorbing the meaning of the preposition into the verb than implying that meaning through the verb.

"The person with whom I had a fight last week is now a friend"

I find this translation better than any attempt to simplistically duplicate the sentence structure:


  上星期和我打（了一）架的那个人现在成了我的朋友。


The key here is that unlike in the original sentence, "the person" is now the implicit subject of the relative clause. This technique works trivially when the clause describes a reciprocal action with "with". Sometimes, even if the action is not reciprocal, you can also get it to work by replacing the verb of the clause with its antonym. For example, for


  The person I sold my bike to also lives in China.


you can say


  买了我的自行车（的）那个人也住在中国。


Comparing with a sentence using the "dummy variable" approach mentioned by Joe,


  我卖了自行车给他的那个人也住在中国。


the former just sounds much more natural and less twisted.

How about "all those sentences that require with/to/etc."?

The two examples above show that you need to adapt the expression to the meaning of the preposition of the clause. But the way of adapting is different in the two examples. I doubt that general rules exist for all such sentences even though I am no linguist. But perhaps there exists this one technique that in many, even if not all, cases can at least make you sound less awkward and more comprehensible with little effort---use more than one sentence. For example, again consider the "sold my bike" example above. You can use these two sentences:


  我把自行车卖给了一个人。那个人也住在中国。


which are totally fine and even easier to understand than "我卖了自行车给他的那个人……". This sacrifices on structural "信" in order to gain on semantic "达" and "雅" of Yan Fu's principles of translation. Sometimes, especially for complex sentences, this is probably the only sensible solution.