Coltsfoot, Comfrey, Ginseng & Goldeseal Culture

I am very interested in growing comfrey and coltsfoot, but I was curious exactly how to get them to germinate?

Comfrey is relatively easy to germinate, just keep the seed bed moist and warm (e.g. with the seed box placed above a heating outlet) and 15 to 20% should germinate in 8 to 9 days. Comfrey is a sporadic germinator, meaning that seedlings appear here and there over a 4-6 week period and not in one flush of growth as is the case with many other herbs and vegetables. Also, total germination is rarely more than 50%
Coltsfoot likes a pH avove 7 so do not use peat in your mix. Sow it as soon as you receive it then place the seed flat in a shady spot outside where you won't forget to keep it moist. The seedlings should germinate in the spring.

Also, in my previous attempts at growing medicinal & culinary herbs, I have absolutely no trouble germinating seeds (except for those that require heat), but once they have germinated I am clueless on what to do, and all my seedlings die. Could you give me some advice on what to do after they have sprouted?

Probably the number one reason for lack of success after successful germination is insufficient light. Most herbs can germinate in relatively low light, but strong seedling development after germination requires stronger light. Untimely watering is a close second reason for lack of success post-germination: missing a watering just once can mean death to small tender seedlings. Be sure to keep the soil of seedlings barely damp, because they have small root systems and dry out to the point of no return, very quickly.
You may also have problems with damping-off fungi. Most of these pathogens swim in water from one plant to the next. So keep your mix just barely moist and it may be a good idea to use sterilized soil to give the seedlings a chance to get stronger before they have to battle fungi. To sterilize soil, wet it in the oven-proof pan, then cook at 400 degrees Fahrenheit for one hour. The odour will be awful! Alternatively, you can buy commercial sterilized sowing mixes from garden centres.
It is worth noting that if you sow seeds outside in garden soil the pathogenic fungi are usually kept in check in healthy, balanced soils by other, harmless micro-organisms and your seedlings should be fine. However, often it is better to start seedlings in containers in sterilized soil because medicinal herbs tend to be slow to establish and in the garden they can easily be overwhelmed by competing weeds.

Last of all, can the ginsengs and goldenseal survive under willow trees (white and weeping)?

I have never heard anything to the contrary. They should love it as long as the soil is humusy and moist. The humus should be of hardwood origin other than aspen.