Colour, strokes and appearance
Shortcuts below are written in their macOS form. On Windows, read ⌘ as Ctrl, ⌥ as Alt and ⇧ as Shift.
Fill and stroke
Two overlapping chips at the foot of the toolbar hold the fill and the stroke. Click either to open a colour picker; the one in front is the side that keys and panels act on. Press X to bring the other side forward, ⇧X to swap the two paints, / to set the front side to none, and D to return to a white fill, a black stroke and a 1 pt weight. The Eyedropper (I) copies a whole appearance from the object you click; hold ⇧ to take only its colour into the active side, or ⌥ to push the selection's appearance onto the object under the pointer.
The Color and Swatches panels
The Color panel (F6) holds sliders in Grayscale, RGB, HSB, CMYK or Web Safe RGB, a hexadecimal field, and a spectrum you can click or drag across. Invert and Complement rework the current colour. In Web Safe RGB a warning triangle appears when the colour is not web safe; click it to snap to the nearest one. When the active side is painted with a global swatch, a tint slider appears above the sliders.
The Swatches panel lists the document's swatches as a grid or a list. A click paints the active side; ⇧-click picks a run and ⌘-click adds or removes one. Double-click a swatch for Swatch Options, where it can be a process or a spot colour; Global keeps the artwork linked to a process swatch, so recolouring the swatch repaints everything painted with it, and spot colours are always global. Every document also starts with a fixed [Registration] swatch, which has no colour type of its own. Drag swatches onto a colour group to file them, or make a group from what you have picked. The panel menu adds the colours already used in the document or in the selection, and selects every swatch nothing uses.
Gradients
The Gradient panel (⌘F9) makes linear, radial and freeform gradients. Click the thumbnail to fill the selection, set the type, reverse the ramp, and work the ramp itself: click it to add a stop, drag a stop to move it, drag a diamond to shift where two colours meet, and set Opacity, Location, Angle and, for radial gradients, Aspect. A freeform gradient can string its points into lines.
With the Gradient tool (G) the same controls sit on the artwork. Drag across an object to lay down the axis, holding ⇧ to hold it to 45° steps. Click the axis to add a stop in the colour it already has there, drag a stop along it, and pull a stop well clear of the axis to throw it away. Drag a diamond to move the midpoint, and drag the round start knob or the square end knob to move either end. Delete removes the stop you last touched. On a freeform gradient, click the artwork to drop a colour point, drag one to move it, and press Delete to take it away.
Strokes, brushes and patterns
The Stroke panel (⌘F10) sets weight, butt, round or projecting caps, mitre, round or bevel corners with a mitre limit, and alignment to the centre, inside or outside of the path. The profile menu tapers the stroke and draws the taper beside it; you can run a profile the other way, save a hand-shaped stroke as a profile, or delete one you made. Dashed Line takes three dash and gap pairs. The Width tool (⇧W) shapes a stroke directly: drag away from the path to widen it there, towards it to narrow it, leaving a width point behind.
The Brushes panel (F5) holds calligraphic, scatter, art, bristle and pattern brushes. Click one to paint the selected paths with it; the Paintbrush uses whichever is current. Double-click for its options, or remove the brush to return strokes to plain lines.
Turn artwork into a tile with Object › Pattern › Make, then fill any shape with it. Tile Options sets the tile type, brick offset, size and spacing. Edit Pattern opens the tile in place, with the copies repeating around it as you work; click Done Editing in the Patterns panel when the tile is right.
Appearance, styles and transparency
The Appearance panel (⇧F6) lists a single object's fills and strokes, topmost first, with any live effects above them. Each row has an eye to hide it, a paint chip, an opacity field, a stroke weight where it applies, and arrows to move it up or down the stack. Add Fill and Add Stroke put another one on top. Object › Expand Appearance bakes the stack into plain artwork.
The Graphic Styles panel (⇧F5) keeps the fills and strokes you save from the selection. Click a chip to apply it; ⌥-click to delete it.
The Transparency panel (⇧⌘F10) sets opacity and the blending mode, from Normal through Multiply, Screen, Overlay and Difference to Hue, Saturation, Color and Luminosity. Isolate Blending and Knockout Group govern how a group blends with what is beneath it. Make Mask turns the topmost selected object into an opacity mask: where it is light the artwork shows, where it is dark it fades out.
Recolouring artwork
Edit › Edit Colors › Recolor Artwork… lists every colour in the selection with how often it is used. Click the chip on the right of a row to choose what that colour becomes, or the arrow between them to leave it alone. Hue, Saturation and Brightness sliders shift the lot together, and two buttons shuffle the order or randomise saturation and brightness. The artwork updates as you go, and Reset returns to the colours it started with. The same submenu also offers Blend Front to Back, Convert to Grayscale, Invert Colors and Saturate.