I am looking for the best and most practical suggestion as to what any average person can implement on a daily basis to help bring Moshiach. This could be either a positive action or refraining from a negative action. Please provide sources for why your answer should be effective, and be specific as to why you think your answer is most practical.
In short, do Mitzvot. The Rambam writes (Teshuva 3:4):
Accordingly, throughout the entire year, a person should always look at himself as equally balanced between merit and sin and the world as equally balanced between merit and sin. If he performs one sin, he tips his balance and that of the entire world to the side of guilt and brings destruction upon himself.
[On the other hand,] if he performs one mitzvah, he tips his balance and that of the entire world to the side of merit and brings deliverance and salvation to himself and others. This is implied by [Proverbs 10:25] "A righteous man is the foundation of the world," i.e., he who acted righteously, tipped the balance of the entire world to merit and saved it.
This article brings lots of practical suggestions of Mitzvot that are "Particularly Propitious for Hastening the Redemption". It brings sources from our sages about various Mitzvot that were told bring the Redemption.
Here's a bullet point list of some of them, see there for more, as well as explanations and sources:
"Even if the Jews have only the yearning for Moshiach, they are worthy of redemption" --Midrash Yalkut Shimoni.
"If Israel does teshuvah, they will be immediately redeemed." --Talmud (Sanhedrin 97B)
"Great is charity for it hastens the Redemption" --Talmud, Bava Batra 10a.
Love and Kindness
"Why was the Temple destroyed? Though the Jews were involved in Torah, mitzvot and acts of kindness, they were guilty of harboring baseless hatred towards each other" --Talmud, Yuma 9b.
Study Jewish Law
"The ingathering of all these exiles will be only in the merit of the Mishnah" --Midrash Rabbah, Leviticus 7:3.
See (and Thank G-d for) the Miracles
"G‑d wished King Hezekiah to be the Moshiach. Said the Attribute of Justice to G‑d: 'Hezekiah, for whom You performed so many miracles, has not sung Your praise. You will make him Moshiach?!'" --Talmud, Sanhedrin 94a.
""The Son of David will not come until the heavenly soul repository is emptied" --Talmud, Yevamot 62a.
- Keep Shabbat (and encourage others to do the same)
- Learn Torah -- From the Ohr HaChayim HaKadosh quoted in this answer.
Be as machmir (stringent) with mitzvos bein adam lechavero (commandments concerning interpersonal relations) as most people are with mitzvos bein adam leMakom (commandments concerning Divine service).
We lost the first Beis HaMikdash because of Avoda Zara (Yoma 9b). Correcting this sin brought us the second Beis HaMikdash.
We lost the second Beis HaMikdash because of Sinas Chinam (ibid). It stands to reason that we must correct this sin to bring the third.
For practical approaches to this, I would personally recommend in-depth study of Likutey Moharan (especially ל״מ א:רפב) and Chofetz Chaim.
The Baal Shem Tov wrote in a letter to his brother in law that he went up to the spiritual palace of Moshiach and asked him "When will you come?"
Moshiach answered him "When your teachings will be spread out and will become known in the world, and your wellsprings (of what I taught you and what you understand) will be spread out, and everyone will be able to do Yichudim and Alyiyos like you. Then all of the Klipos will be destroyed, and the time will be auspicious for the redemption".
We are not allowed to "bring Moshiach" or do anything which would "hasten the End", as the Rashbash (Shailos v'tshuvos #2) writes:
אמנם מצוה זו אינה מצוה כוללת לכל ישראל בגלות החל הזה, אבל היא נמנעת כלל כשז"ל בגמרא כתובות פרק האחרון שהיא מכלל שבועות שהשביע הקדוש ב"ה את ישראל לא ימהרו את הקץ ושלא יעלו בחומה, וצא וראה בני אפרים מה קרה להם שמהרו את הקץ
"that we are are not allowed to "hasten the end" and see what happened to the children of Ephraim who hastened the End."
The bnei Ephraim were said to have left Egypt earlier than they were supposed to and were described as דוחקי הקץ, people who forced or hastened the end. (For more info see here)
So our mission is just to keep the Torah and not worry about God's plans for the End; the idea that we should actively attempt to bring about the End is highly problematic.
Stop lashon hara, stop accepting lashon hara. I'd say this is the #1 thing keeping Moshiach from coming, if we stop lashon hara, we stop senseless hatred, and ahavat yisroel is our biggest motive for bringing Moshiach. Learn Kabbalah, study Chofetz Chaim (laws on lashon hara), Mussar, and give Tzadakah! Make that 10% into 15%. And finally, motivate others to do the same!
Learn Days Are Coming by Rabbi Moshe Silberstein.
It’s an In-Depth Analysis of the Practical Halachos Relevant to Visiting the Bais HaMikdash.
Why? The Chofetz Chayim says, “If we were truly yearning for the final Redemption and waiting each day for its arrival, then we would be preparing ourselves by learning the relevant halachos, for there are many halachos to be learned and they cannot all be covered in a short time… For if it would be revealed that in a short time the final Redemption would arrive, then certainly millions of Jews would quickly learn the halachos to the Beis HaMikdosh, since at that time all of these halachos will be applicable, not only for kohanim but for all Jews, for instance, the halachos regarding eating karbonos and visiting the Mikdash… Therefore, if we are truly waiting and yearning for the final Redemption… we too should arouse ourselves and learn these halachos with all our strength” (Torah Ohr, chapter 12)
Another seifer that one can learn is Geulah BeRachamim by Rabbi Pinchas Winston. It contains 60 daily lessons to yearn for redemption. Yearning for redemption is not only a mitzvah, it is crucial for surviving the events at the End-of-Days. How does one develop such a yearning? By reading this book and taking its 60 lessons to heart.