How does exercising/starved muscle import glucose (released by liver)?
GLUT4 is the major glucose transporter in muscle even in exercise. However, during exercise, it is translocated to the cell surface by contraction-triggered, insulin-independent mechanisms, such as AMP-activated protein kinase (AMPK) activation.

For more, you could read this review.

Note:

'No insulin' is too strong a phrase; exercise and fasting are associated with low but detectable insulin levels. The reference range for fasting insulin in healthy individuals is $&lt;174 \ \text{pmol L}^{-1}$ (contrast this with levels upto $1917 \ \text{pmol L}^{-1}$ one hour after glucose ingestion). Exercise studies have shown levels around $60-80 \ \text{pmol L}^{-1}$.