Boaz said to Rus, "Hear me well, my daughter. Do not go to gather in another field, and don't leave here, but stay here close to my workers. Keep your eyes on the field which they are harvesting and follow behind them, I have ordered the young men not to bother you".
We need to understand why Boaz would need to order his workers not to bother Rus, who was a simple widowed convert who came picking in their field. Why should they want to bother her? Furthermore, because the Torah specifically forbids one from upsetting a widow, and Boaz's workers were definitely righteous and would be most meticulous about this transgression, how much more so should Boaz not need to warn them. And lastly, what is the connection between Boaz's instructions to Rus that she should 'keep her eyes on the field which the workers are harvesting and follow behind them', to the fact that 'he has ordered the young men not to bother her'?
There is a mitzvah to leave the shich'chah, which is bundles that were skipped over and bypassed during the process of collecting the bundles, in the field for the poor people to gather. The Passuk (דברים כד יט) describes the laws of shich'chah, as follows.
כי תקצר קצירך בשדך, ושכחת עמר בשדה, לא תשוב לקחתו, לגר ליתום ולאלמנה יהיה וכו'.
When you reap your harvest in your field, and you forgot a bundle in the field, you shall not go back to take it; it shall be for the convert, the orphan, and the widow...
The Mishnah in Pe'ah (ו ד) derives the following Halacha regarding what is considered shich'chah, from the wording of this Passuk.
זה הכלל כל שהוא בבל תשוב שכחה. ושאינו בבל תשוב אינו שכחה
This is the rule: Whatever is governed by 'do not turn back' is shich'chah; whatever is not governed by 'do not turn back' is not shich'chah. [i.e. Shich'chah only applies to a bundle that was forgotten in such a way that its retrieval involves turning back.]
The Mishna brings an example to illustrate this Halacha.
שנים שהתחילו מאמצע השורה, זה פניו לצפון וזה פניו לדרום, ושכחו לפניהם ולאחריהם, את שלפניהם שכחה, ואת שלאחריהם אינו שכחה
Two workers who decided to start collecting the bundles somewhere in the middle of a row, and to work their way in opposite directions to the two ends of the row, and they bypassed bundles in front of them and behind them; those bundles which are in front of them are deemed shich'chah [i.e. as they constitute the typical shich'chah, for these bundles were in front of the worker who was making his way toward them and who then bypassed them. They were thus skipped over and forgotten and may not be retrieved.] while those which are behind them are not deemed shich'chah [i.e. because those bundles had never been within the routes of the workers, for they started collecting beyond it, and thus were never forgotten, but were completely outside the workers' route].
Accordingly, we can explain Boaz's directives to Rus and what he needed to warn his workers about as follows. When Boaz told Rus, "Keep your eyes on the field which they are harvesting and follow behind them", he was instructing her to do the following. He was telling her that out of modesty, it wouldn't be appropriate for her to stand in front of the workers waiting for them to skip over some bundles, but rather she should stand behind the area where the workers are working. And although by standing behind their area of work she'll never have the opportunity to collect any shich'chah, for any bundles that lay behind where they work is not forgotten and not passed over, nevertheless with this directive he was essentially giving her explicit permission to collect bundles which technically are not rendered shich'chah.
In view of this we can understand why Boaz needed to warn his workers not to bother Rus. For when they would see her collecting bundles which aren't shich'chah, they would automatically assume she wasn't behaving with the utmost honesty, and they would thus take matters into their hands and not let her collect the bundles from beyond their work area.
Accordingly, we can also understand the correlation in Boaz's words. For it was only because he instructed Rus to 'follow behind the workers', and to thus collect bundles which cannot be considered shich'chah, that he needed to 'order the young men not to bother her'.
(זרע שמשון מגילת רות אות ג)
