Does being charged with trespassing affect my citizenship process?

In the naturalization application process you would be required to reveal the trespassing offense and supply court-certified copies of all the disposition documents (and the trespassing offense also would be revealed to the USCIS through the security background check process). Since you were ordered to pay a fine and paid it, the USCIS will treat it as a conviction for that offense. While a full review of the disposition documents would be necessary in order to reach a definitive answer, generally if that is the only "blemish" on an applicant's record, and especially if the offense took place more than five years ago, it should not stand in the way of eligibility to naturalize. It would be wise to consult with an immigration attorney who, after reviewing the actual disposition documents and learning all other relevant information, could advise you about eligibility to naturalize as well as advise you about whether providing documentary evidence of good moral character (such as volunteering for charitable causes) would be helpful in persuading a USCIS adjudicating officer that you do not "lack good moral character" as that phrase is used in the regulations. Some immigration law firms, including mine, offer legal services on a "flat fee" basis so that a client will know the total expense from the very beginning, and a few immigration law firms, including mine, offer an initial consultation free of charge.

It should not. However, you need to obtain a certificate of disposition and show it to an Immigration attorney.