It took me and my Korean-speaking dad 3 days of bumbling to figure all this out. With this guide, you can do it all in one afternoon.

(Note, this is similar to Edd's post from 29Jul2013...but I only found his post today)

Step 1: INSURANCE

Get this several days before your bike arrives! Two options:

Wendy Choi (speaks English) wendy@aerointl.kr
W82000 for up to 1 week

Byung Geun Chun (speaks English)
Samsung Expat Insurance Team
Mobile 010-3232-0625
Company email: bgchun@samsungfire.com

You need:
License
Title/Registration
Passport
Dates of policy
Name of departure vessel (e.g. DBS Ferry Eastern Dream, Donghae-Vladivostok)
Invoice showing value of motorcycle (can be made up)

Step 2: AIR WAYBILL

Take subway to Incheon Air Cargo Terminal subway stop
Exit 1, up escalator, turn left
Free shuttle "for IACC" to cargo terminal

Terminal A Korean Air
Terminal B Asiana
Terminal C Foreign Carriers

I shipped via Qatar Airways and entered Air Cargo Terminal C, entrance C, near the glass elevator. Upstairs to "Asiana Airport" office on 1st floor (2nd American floor) (37.469899,126.465437)

Present printed copy of Air Waybill and exchange for stamped original Air Waybill

If necessary, go to office on 2nd floor (3rd American floor) with beige door marked "IRR" (irregularities?) in case of suspected damage during shipment. My bike was leaning heavily on its pallet but there was no real damage.

Step 3: CUSTOMS

Take free shuttle "for Terminal 1" East Entrance, Level 3 Door 3
(37.449399,126.453563)
Take elevator down to B1

Terminal 1 Level B1 Room B088
"Customs Baggage Clearance"
Near "Spa On Air"

Talk to Kim Juwon (green polo shirt, big desk)

You need:
Air Waybill
License
Title/Registration
Passport
Proof of insurance
Some form of invoice showing your bike's value
Maybe International Drivers Permit
Maybe Russian Visa page, if necessary

Go upstairs to pay non-refundable fee to Kookmin Bank ATM
Account 630-009231-643

1-500cc KRW120000
500-1100cc KRW160000
1100+cc KRW240000

Receipt is proof of payment!

TIP is valid for period of insurance validity

Receive yellow "sticker" (paper circle)

Step 4: PICK UP BIKE!

Free shuttle "for IACC" back to applicable cargo terminal

Present TIP and Air Waybill to your cargo airline's office
Paid W101500 for 27 hrs warehouse storage (W50000/24hr, no partial days)

Present TIP and Air Waybill at ground floor warehouse to retrieve bike

Receive your bike!

DON'T LET THEM TAKE YOUR ORIGINAL TIP!!! They can make copy; you take original. Keep your yellow paper 'sticker' too.

Stop at toll gate to exit cargo terminal area and you'll be waved through.

Incheon ICN airport is on an island. There are two bridges on/off the island, but both are expressways and motorcycles are prohibited.

Ride Sejong Yeongdong Ferry (+82 777 8087) to mainland
(37.492576,126.580925)
Park in the left lane and buy your ticket at the short grey box building back at the intersection
7:30am-6:30pm, hourly (weather permitting), KRW6000 for 1 bike 400cc+ and 1 person (extra person KRW3500)

QUICK TIPS:

1) Right turn on red is PERMITTED after a full stop
2) Gasoline/petrol (hwe bal yoo) is the YELLOW pump
3) All gas stations take credit cards
4) Motorcycles not permitted on Korean expressways! Local roads only
5) Keep your TIP and yellow "sticker" in a safe place--both are required at customs to leave Korea
6) Google Maps driving navigation doesn't work in Korea, neither offline nor online. Most Koreans use Naver Maps, but most points of interest are only in Korean.

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Nice and simple then haha.
Fantastically thorough thank you.
How difficult is it to get around the country if you can't use the expressways (I assume that's like motorways in UK?)

Oh sorry, just now saw your questions.

I use the word "expressway" here to mean the roads where there are no 90-degree intersections, and only on- and off-ramps. Even within the US we use the words expressway, highway, and freeway to describe these roads, depending on region. My best knowledge of British English is that yes, those would be the same as 'motorways'.

In and around the Seoul area, progress on local roads is achingly slow with stop-and-go traffic and stoplights for hours. Outside Seoul, much better but you still need to go through every intermediate-size city along the way.

There were some times when the non-freeway roads suddenly became freeways with minimal notice (and didn't show up that way on OSM), only to change back to 'local' roads a short while later, but I just kept riding because navigating a way around those short sections would be a pain in the ass.

Korea is a relatively small country though, so even riding only local roads you can still make reasonable progress in a day.