I actually have this situation, dude I work with asked me about 6 months ago. Been training him and sorting his diet since then and he has gained around 25lb, was terribly skinny before and weak and ate like a baby bird. Most of the weight has been good quality muscle
push pull was my go to routine
front leg kick 4x10reps
close hand press up 3 sets to failure
chin up 4x as many as possible
bent over row 3x10reps
ham curl 3x10reps
bicep curl 4x10reps
alternate these two work outs, training 3 times a week
Run this for 3 months to learn movements and hone technique. 4 second negatives on all exercises except deads. Increase weight when full rep target is are achieved without sacrificing form or tempo.
After 3 months it's good old 5x5 until a good level of strength is achieved.
In terms of diet I'm a firm believer in being reactive to results and building from the persons current diet. In most situations people are eating at a point of maintenence without trying, so they won't be losing or gaining and there weight is pretty much settled. Rather than changing the whole diet it's better to add a couple of easy things and assess results
for example, for the person above I added a shake in the morning with 40g of protein 80g of oats and a shot of olive oil, and a shake before and after training of plain whey. After a 3 weeks it was obvious it wasn't enough as the scale had not moved. The addition of an extra meal in the day of rice, meat and veg and the scale started moving again.