From Agnew meadows take trail past Shadow Lake to Ediza Lake. Ascent is half day from there or a full day from Agnew Meadows.
I'm at work doing this from memory without topos or books in front of me so excuse any errors but the route is straight forward and pretty easy so here it goes. Head West from Ediza Lake past a small tarn and continue towards the Ritter-Banner Saddle. You will come to some cliffs were you will be forced to veer slightly to the North in order to avoid technical climbing. The climbing in here is easy although there is annoying loose rock and sand below you. Once the cliffs are bypassed you come to a permanent snowfield/mini glacier (when I climbed it in mid October the bergschrund was about an inch and a half wide!). Depending on conditions an ice axe may be all you need or crampons may be helpful later in the year (I was glad to have them for the snow was rather firm/icy and suncupped). As you ascend the snowfield you will notice a tongue that ascends to the northwest at a steeper pitch (Class 3 as I have read). Ascend that short pitch to the Saddle. From here you can easily walk to the Western slope of Banner Peak. The ascent from here requires only route finding (somewhat tricky) and stamina. As you climb the Western Face, cheat to the left (North) side. A nice view of Thousand Island Lake from the top. Descend the same way. I have no pictures to upload but there are helpful photos already on the Banner Peak page.
Ice axe definitely and crampons depending on conditions.
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