Before casting on, you need to calculate how many blocks you want in your fabric and how many stitches will be there in each block. Example, each block contains 6 sts, and each tier contains 5 blocks, so you cast on 30 sts.

For this tutorial, starts with 18 sts to be worked in three groups of 6.
THREE BASE TRIANGLES
Row 1: (RS) K1, turn
Row 2: Purl sts in this section, turn
Row 3: SL 1, K1, turn
Row 4: Purl sts in this section, turn
Row 5: SL 1, K2, turn
Row 6: Purl sts in this section, turn
Row 7: SL 1, K3, turn
Row 8:  Purl sts in this section, turn
Row 9: SL 1, K4, turn
Row 10: Purl sts in this section, turn
Row 11: SL 1, K5, do not turn
End of base triangle one of three, start next base triangle on next stitch.
Rep Rows 1 to 11 two more time to complete all three base triangles.
TIER 1: 2 Diamonds and 2 Side Triangles 

Left Side Triangle 
Row 1 (WS): K1, turn
Row 2: Kfb, turn
Row 3: K1, P2tog, turn
Row 4: K1, M1, K1, turn
Row 5: K1, P1, P2tog, turn
Row 6: Knit to last st, M1, K1, turn
Row 7: K1, P2, P2tog, turn
Row 8: Knit to last st, M1, K1, turn
Row 9: K1, P3, P2tog, turn
Row 10: Knit to last st, M1, K1, turn
Row 11: K1, P4, P2tog, do not turn
Now work the two middle diamonds of Tier 1.

Two Middle Right SLanting Diamonds 
Row 1 (WS): With WS facing, pick up and purl 6 sts along the selvedge edge of the next triangle. Slip last st picked up onto the left needle and P2tog, turn.
Row 2: K6, turn
Row 3: SL1, P4, P2tog, turn
Row 4: K6, turn
Row 5: SL1, P4, P2tog, turn
Row 6: K6, turn
Row 7: SL1, P4, P2tog, turn
Row 8: K6, turn
Row 9: SL1, P4, P2tog, turn
Row 10: K6, turn
Row 11: SL1, P4, P2tog, do not turn.
Rep Rows 1 to 11 one more time to complete all both middle diamonds. Once both diamonds are done began working the right side triangle in the next section.

Right Side Triangle 
Row 1 (WS): With WS facing, pick up and purl 6 sts along the selvedge edge of the next triangle or diamond, turn.
Row 2: Knit sts in this section, turn
Row 3: SL1, P3, K2tog, turn
Row 4: Knit sts in this section turn
Row 5: SL1, P2, K2tog, turn
Row 6: Knit sts in this section turn
Row 7: SL1, P1, K2tog, turn
Row 8: Knit sts in this section turn
Row 9: SL1, K2tog, turn
Row 10: Knit sts in this section turn
Row 11: K2tog, turn
Transfer this st to the right needle.
The remaining stitch will be counted as the first st picked up for the first diamond in Tier 2.

TIER 2: 3 Diamonds 

Three Left SLanting Diamonds 
For the first diamond only, the remaining stitch from the last tier counts as 1 picked up stitch
Row 1 (RS): With RS facing, pick up and knit 6 sts along the selvedge edge of the next triangle or diamond. Slip last st picked up onto the left needle and SSK, turn.
Row 2: P6, turn
Row 3: SL1, K4, SSK, turn
Row 4: P6, turn
Row 5: SL1, K4, SSK, turn
Row 6: P6, turn
Row 7: SL1, K4, SSK, turn
Row 8: P6, turn
Row 9: SL1, K4, SSK, turn
Row 10: P6, turn
Row 11: SL1, K4, SSK, do not turn
Rep Rows 1 to 11 two more times to complete three middle diamonds. Once the three diamonds are done you will start tier one again.
Continue working tiers 1 and 2 until the desired length is reached. 

BIND OFF TRIANGLES
Before you begin the bind off triangles the last tier you work is tier one. 
Row 1 (RS): With RS facing, pick up and knit 6 sts along the selvedge edge of the next triangle or diamond. For the first triangle only, the st remaining counts as the first picked up stitch.
Slip last st picked up to left needle and SSK, turn.
Row 2: Purl sts in this section, turn
Row 3: K2tog, K3, SSK, turn
Row 4: Purl sts in this section, turn
Row 5: K2tog, K2, SSK, turn
Row 6: Purl sts in this section, turn
Row 7: K2tog, K1, SSK, turn
Row 8: Purl sts in this section, turn
Row 9: K2tog, SSK, turn
Row 10: Purl sts in this section, turn
Row 11: SKPO, do not turn.
The remaining stitch will count as the first stitch of the next triangle.