Different ways Shikantaza is taught
Over the last 1.5 years that I studied Zen, here are the main/popular ways "Shikantaza" was taught by different teachers/lineages
Breath following Group: Focus your attention on "following the breath", usually at the hara. Count your breaths initially and then move onto following the breath without any counting. Finally sit shikantaza style
Lineages: Suzuki Roshi (Sanfrancisco Zen Center), Mauzemi Roshi (Zen center of Los Angeles) and many others in the US and Japan. This is the most popular way it is being taught now.
"Nothing but Sitting": This is same as what is mentioned in "Opening the hand of thought". This is definitely a method. There is no object though. If anything, the object is "your reality of sitting and facing the wall". You keep coming back to this, waking up from anything else that is happening other than this (distracted thinking, drowsiness etc).
Lineages: Kodo Sawaki Lineage. Kosho Uchiyama and Okumura made this popular. Chan's methodless method also sounds very similar to this, except that the object is "being aware of your whole body sitting there". I think Jundo teaches this. Many other teachers that teach shikantaza style recommend this.
"Simply Sit, let go of control": My favorite. You simply sit and let go of any conscious control of your meditation. Don't try to do anything to meditate better. This is also known as a practice of great faith. You sit with the trust/knowing that whatever happens is okay. That sitting sits itself. Doesn't need your intervention. You firmly believe sitting to be a useless practice and that it doesn't add anything to you. Tomorrow is not going to be any better than today. Nowhere to go. Nothing in need of change. To simplify, however you sit is fine, as long as there is no conscious activity or focus on an object or a method you are trying to follow.
Teachers: Not many modern teachers recommend sitting this way. Few that I have personally met. Daigaku Rumme (Zenshuji of Los Angeles), Jyozen Anjyu (Kanzeonji buddhist temple, Los Angeles), Brad Warner, Kevin (another student of Nishijima from Los Angeles). Jundo too suggests this but he mixes this with "Nothing but Sitting". Some teachers asking students to sit without any instructions fall into this category i believe (Antaiji, Taigu sometimes). ofcourse Dogen :)
Use of other objects: Use of sound as an object is pretty popular after breath. Many teachers recommend the use of some object before their students can sit shikantaza.