How do I convert from unicode to surrogate pairs?

I'm not sure you really understand what the surrogate pairs are meant for. They just encode the exact same unicode code point just as two 16 bit pairs. It's explained pretty well on wikipedia. So if you have a unicode code point you first subtract 0x10000. The remaining number is split into two 10 bit numbers, one low and one high pair. You add D800 to the high bits and DC00 to the low bits. In your specific example

 1F601
 binary representation
 0001 1111 0110 0000 0001
 
 When we subtract 0x10000 we get
 0F601
 or
 0000 1111 0110 0000 0001
 
 The high bits are 0000 1111 01, the low bits are 10 0000 0001
 
 To get the high surrogate we just combine D800 (1101 1000 0000 0000) with the high bits
 
 1101 1000 0000 0000 // D800
 0000 0000 0011 1101 // 003D
 ---------------------------
 1101 1000 0011 1101 // D83D
 
 To get the low surrogate we do the same thing with DC00
 1101 1100 0000 0000 // DC00
 0000 0010 0000 0001 // 0201
 ---------------------------
 1101 1110 0000 0001 // DE01

In plain C# it would look something like that:

 int cp = 0x1F601;
 cp -= 0x10000;
 int high = 0xD800 | ((cp >> 10) & 0x3FF);
 int low = 0xDC00 | (cp & 0x3FF);

However C# does already have a method that does this conversion char.ConvertFromUtf32.

Note that all this is irrelevant if your used font does not support those code points you're trying to display. Also note that there is no font that supports all unicode code points