The Joy-Con use bluetooth or a wired connection to communicate with the console, depending if they are physically connected to it or not.
dekuNukem has started RE on the protocols used [1].

Firmware

The firmware of the Joy-Cons seems to be generic across all instances. Details such as the handedness of the controller and the color is just indicated in a configuration part of the flash. Judging by quick glance at the firmware, it's probably identical to that used on the Pro Controller as well.

Controller 1.0.0
Joy-Con Left (Blue) flash dump
Joy-Con Right (Red) flash dump

The flash is in a patch-ram format. Tools for dealing with it are available [2]. A dump of the ROM region (taken while firmware was running) can be found here. Note this is the same SoC used on the other controller models, as well.

Left & Right Separate Joy-con

When paired directly to a computer over bluetooth, the joy-con both provide identical HID input report descriptor. This does not appear to include motion controls, IR data, or NFC. They both behave as detached single-player controllers.

HID Input Report Descriptor (Hexadecimal):

00000000: 05010905 A1010601 FF852109 21750895  ....¡...ÿ…!.!u.•
00000010: 30810285 30093075 08953081 02853109  0..…0.0u.•0..…1.
00000020: 31750896 69018102 85320932 75089669  1u.–i...…2.2u.–i
00000030: 01810285 33093375 08966901 8102853F  ...…3.3u.–i...…?
00000040: 05091901 29101500 25017501 95108102  ....)...%.u.•...
00000050: 05010939 15002507 75049501 81420509  ...9..%.u.•..B..
00000060: 75049501 81010501 09300931 09330934  u.•......0.1.3.4
00000070: 16000027 FFFF0000 75109504 81020601  ...'ÿÿ..u.•.....
00000080: FF850109 01750895 30910285 10091075  ÿ…...u.•0‘.…...u
00000090: 08953091 02851109 11750895 30910285  .•0‘.…...u.•0‘.…
000000A0: 12091275 08953091 02C0               ...u.•0‘.À
Parsed Bytes Description
0x05, 0x01, Usage Page (Generic Desktop Ctrls)
0x09, 0x05, Usage (Game Pad)
0xA1, 0x01, Collection (Application)
0x06, 0x01, 0xFF, Usage Page (Vendor Defined 0xFF01)
0x85, 0x21, Report ID (33)
0x09, 0x21, Usage (0x21)
0x75, 0x08, Report Size (8)
0x95, 0x30, Report Count (48)
0x81, 0x02, Input (Data,Var,Abs,No Wrap,Linear,Preferred State,No Null Position)
0x85, 0x30, Report ID (48)
0x09, 0x30, Usage (0x30)
0x75, 0x08, Report Size (8)
0x95, 0x30, Report Count (48)
0x81, 0x02, Input (Data,Var,Abs,No Wrap,Linear,Preferred State,No Null Position)
0x85, 0x31, Report ID (49)
0x09, 0x31, Usage (0x31)
0x75, 0x08, Report Size (8)
0x96, 0x69, 0x01, Report Count (361)
0x81, 0x02, Input (Data,Var,Abs,No Wrap,Linear,Preferred State,No Null Position)
0x85, 0x32, Report ID (50)
0x09, 0x32, Usage (0x32)
0x75, 0x08, Report Size (8)
0x96, 0x69, 0x01, Report Count (361)
0x81, 0x02, Input (Data,Var,Abs,No Wrap,Linear,Preferred State,No Null Position)
0x85, 0x33, Report ID (51)
0x09, 0x33, Usage (0x33)
0x75, 0x08, Report Size (8)
0x96, 0x69, 0x01, Report Count (361)
0x81, 0x02, Input (Data,Var,Abs,No Wrap,Linear,Preferred State,No Null Position)
0x85, 0x3F, Report ID (63)
0x05, 0x09, Usage Page (Button)
0x19, 0x01, Usage Minimum (0x01)
0x29, 0x10, Usage Maximum (0x10)
0x15, 0x00, Logical Minimum (0)
0x25, 0x01, Logical Maximum (1)
0x75, 0x01, Report Size (1)
0x95, 0x10, Report Count (16)
0x81, 0x02, Input (Data,Var,Abs,No Wrap,Linear,Preferred State,No Null Position)
0x05, 0x01, Usage Page (Generic Desktop Ctrls)
0x09, 0x39, Usage (Hat switch)
0x15, 0x00, Logical Minimum (0)
0x25, 0x07, Logical Maximum (7)
0x75, 0x04, Report Size (4)
0x95, 0x01, Report Count (1)
0x81, 0x42, Input (Data,Var,Abs,No Wrap,Linear,Preferred State,Null State)
0x05, 0x09, Usage Page (Button)
0x75, 0x04, Report Size (4)
0x95, 0x01, Report Count (1)
0x81, 0x01, Input (Const,Array,Abs,No Wrap,Linear,Preferred State,No Null Position)
0x05, 0x01, Usage Page (Generic Desktop Ctrls)
0x09, 0x30, Usage (X)
0x09, 0x31, Usage (Y)
0x09, 0x33, Usage (Rx)
0x09, 0x34, Usage (Ry)
0x16, 0x00, 0x00, Logical Minimum (0)
0x27, 0xFF, 0xFF, 0x00, 0x00, Logical Maximum (65534)
0x75, 0x10, Report Size (16)
0x95, 0x04, Report Count (4)
0x81, 0x02, Input (Data,Var,Abs,No Wrap,Linear,Preferred State,No Null Position)
0x06, 0x01, 0xFF, Usage Page (Vendor Defined 0xFF01)
0x85, 0x01, Report ID (1)
0x09, 0x01, Usage (0x01)
0x75, 0x08, Report Size (8)
0x95, 0x30, Report Count (48)
0x91, 0x02, Output (Data,Var,Abs,No Wrap,Linear,Preferred State,No Null Position,Non-volatile)
0x85, 0x10, Report ID (16)
0x09, 0x10, Usage (0x10)
0x75, 0x08, Report Size (8)
0x95, 0x30, Report Count (48)
0x91, 0x02, Output (Data,Var,Abs,No Wrap,Linear,Preferred State,No Null Position,Non-volatile)
0x85, 0x11, Report ID (17)
0x09, 0x11, Usage (0x11)
0x75, 0x08, Report Size (8)
0x95, 0x30, Report Count (48)
0x91, 0x02, Output (Data,Var,Abs,No Wrap,Linear,Preferred State,No Null Position,Non-volatile)
0x85, 0x12, Report ID (18)
0x09, 0x12, Usage (0x12)
0x75, 0x08, Report Size (8)
0x95, 0x30, Report Count (48)
0x91, 0x02, Output (Data,Var,Abs,No Wrap,Linear,Preferred State,No Null Position,Non-volatile)
0xC0, End Collection

Colors

HEX codes for the colors shown in the "Controllers" menu of the Switch UI can be found in a Joy-con SPI dump starting at offset 0x6050. Body color is first followed by button color and each is 3 bytes long. These values are able to be re-written with any HEX color value to make the Joy-cons show up as different colors in the UI. The following is a list of official HEX colors recovered from SPI dumps.

Color Name Body HEX Button HEX
Gray #828282 #0F0F0F
Neon Red #FF3C28 #1E0A0A
Neon Blue #0AB9E6 #001E1E
Neon Yellow #E6FF00 #142800
Neon Green #1EDC00 #002800
Neon Pink #FF3278 #28001E
Mario Red #E10F00 #280A0A