Layer-by-layer method in 8 steps, 7 algorithms. Full course with animations and simulator: strefa-kostek.pl/en/kursy
U up, F front, R right, L left, DR down-right (below F and R). Letter = 1/5 of a turn clockwise looking at the face, ' the other way, 2 two steps, U2' two steps the other way. The slot you are filling is always at the front right (between F and R), the face above them is U; white face at the bottom (for the star - on top).
White centre on top, 5 white edges, second colour matching the face below.
An edge goes up to the top by turning the upper face it lies next to: in the ring - with the face without the white sticker (1 step); on the bottom edge of a face, white down - 2 steps; white on the upper face - 1 step into the ring. In the lower part: the lower faces do not move the star.
Before turning an upper face, set the top (U) so the spot for that edge is above it; after inserting, undo the top.
Corner at U F R, slot at the bottom front right.
Lower face (DR) colour: to the right R U R' U' ×1, up ×3, to the front ×5. Corner in the wrong slot: ×1 pushes it up.
White: white face = DR. Belt (step 5): the corner's upper face on the right (R), set up with R and grey top turns. Upper (step 7): grey top = U.
Slot at the front right, edge on top next to the slot.
Above F (front colour = F): Right R' U' R F' R' U R F
Above R (right colour = R): Left F U F' R F U' F' R'
Belt (step 6): first park the edge in the ring below the grey face above the slot (grey top, Right/Left, upper-face colour on the upper face), then slide it down: slot's upper face at the front → Right, on the right → Left.
Edge stuck in another slot: push it out with Right using any edge.
F R U R' U' F'
Two flipped with a gap: good one on the right, ×1. Two next to each other: at the front and on the right, ×2. Four: good one at the back left, ×1, then as with a gap.
R U R' U R U2' R'
Top for the most matches. Two next to each other: at the front and on the left, ×1-2. With a gap: gap edge belongs 2 to the right → at the front; 2 to the left → on the left; ×1, start again. One: at the front, ×1, start again.
U L U' R' U L' U' R
Do not turn the top; a corner matches the edges next to it. Two next to each other: at the back, ×1-2. With a gap: the wrong one between the good ones belongs 2 to the right → back left, 2 to the left → front left; ×1. One: at the back right; ×2 if front right is swapped with back left, otherwise ×1. None: the corner that belongs in its right neighbour's spot at the front left, ×1.
Corner at the top front right: R' DR' R DR ×2 or ×4, until grey is on top; turn the top (U) to the next one. The lower faces fall apart along the way and come back at the end; align the top.