The chief way that Milton makes Satan attractive as a character is by giving him 'depth': that is, he has the characteristics that we recognise in ourselves, as fallen human beings. Milton's God, by contrast, though just and good, seems remote and intimidating.
The attractiveness of Milton's Satan has caused problems for many readers. But of course, if evil were repellent, it would not be tempting.
Over the course of the poem, we see Satan in many guises: as a charismatic military leader, a skilled rhetorician, a cunning strategist, even as a kind of courtly lover (look at his overtures to Eve in Book 9). We also see him in the depths of despair, when he recognises the futility of his vengeful campaign against God. To read the poem we need to be active in seeing how Milton manipulates our response to Satan. As soon as we are seduced by his rhetoric and apparent logic, Milton points us to the extent of his deception, and his self-deception. So, although Milton makes Satan attractive, he also gives us the means to see that attractiveness as delusion.
Milton makes Satan attractive by three general routes:
He makes Satan sympathetic. (We see and feel his suffering.)
Satan stands up for autonomy. He's not going to be told what he should do; he's going to do what he wants to do, even if it means going to hell. There's a powerful modern/Romantic appeal there.
He gives Satan pride. This is related to his desire for autonomy. Satan is so proud of who he is that he will stand up for it even when he's going to lose. There's something to admire there.
I think it is important to note that Milton is not the only source that renders Satan as an attractive character. This is Biblical. In the book of Isaiah, Lucifer is addressed as the Day Star, and 2 Corinthians says that "even Satan disguises himself as an angel of light." Milton makes Satan attractive because he has to in order to remain true to the Bible. Doesn't it make perfect sense that the Great Deceiver would pose as a magnificent and beautiful creature, when deep down, he is the essence of evil. Milton says that he is "clothed with transcendent brightness." (line 86) If Satan is truly as seductive as he is supposed to be, then he must be attractive. It is essential.