Hi, You can follow this schedule - Yamunotri -> Gangotri -> Kedarnath -> Badrinath
Day1: Board the bus from Dehradun "pahadi" bus stand to Barkot (135km, approx 4-4.5hrs bus journey)
Board the early morning bus (5-5:30AM) and reach Barkot by ~9AM. From Barkot, board a share cab/ private cab till "Janki Chatti" (45km, ~2hours), you'll reach Janki Chatti by probably 12PM.
From Janki Chatti (2521m), Yamunotri temple is about 5km (Altitude: 3246m). You can do this in like 2-2.5hrs depending upon your capacity or may hire a porter. From Yamunotri you can come down the same day and stay at Janki Chatti.
Day 2: Start early morning and come down to Barkot by a share cab (45km, ~2 hours) or if share cabs from Janki chatti are available till Uttarkashi then well and good. Else from Barkot, board a bus/share cab to Uttarkashi (~80km, 3hours). From Uttarkashi, there are ample of share taxis to Gangotri (~100km, 3 - 4 hours). You will be able to visit the temple the same day. Stay at Gangotri or Harsil and enjoy the day with their local delicacies, maggi and tea.
Day 3: Enjoy the sunrise at Harsil/Gangotri, board a share cab and come down to Uttarkashi (100km, ~3-4 hours). From Uttarkashi, take a share cab till Rishikesh (~170km, 6-6:30hrs). Rest and enjoy Rishikesh.
Day 4: Catch the first bus to Sonprayag from Rishikesh (~212km, ~8hrs). From Sonprayag, several share taxis are available till Gaurikund (~7km). You may either take a share cab or go by foot (depending on your capacity). Stay at Gaurikund.
Day 5: Trek to Kedarnath from Gaurikund (16km trek), start as early as possible (Trek from Gaurikund starts at 4 AM till 1 PM, after 1 PM you are not allowed to trek to Kedarnath from Gaurikund). It's a 16km trek and can be done in a day. Gaurikund is at an altitude of 1985m and Kedarnath at 3543m, there's in an altitude rise of 1558m (5141ft). The route is Gaurikund - Jungle Chatti (4km) - Bheembali (3km) - Linchauli (4km) - Kedarnath base camp (4km) - Kedarnath temple (1km). If you are damn fit then you can do this in a day or else there is a very high possibility of AMS. Keep your pace slow, drink ample amount of water and take black coffee or green tea to keep you fit and motivated. Reach Kedarnath, hire a room and stay there, attend evening prayer and enjoy the scenic beauty.
Day 6: Attend the morning aarti and start descending. Descending would be easier and you can easily descend in like about 6 hours. So lets say that you started descending at about 6AM, you should probably reach down by 12PM or max 1PM. Let's say you reach by 1 PM, take share cab and reach Sonprayag. From Sonprayag take a bus or cab till Rudraprayag (~75km, ~2.5 - 3 hours). Get a room and rest here.
Day 7: Start early, Take any bus coming from Rishikesh to Badrinath (~160km, 5:30 - 6hours). Let's say you reach Badrinath by 2 PM. You can visit the holy shrine, take a dip in the hot springs. You may visit Mana village (4km from Badrinath shrine which is said to be the last Indian village in that area). You may stay at Mana (free from hustle bustle) or may stay at Badrinath.
Day 8: (optional) you may roam in Mana and visit Bhhempul, Vyas gufa, ganesh gufa and other places. Enjoy the place, relax and chill and get down to Joshimath (~50km, 2.5 - 3hours). Get a room and enjoy the place.
Day 9: Start early, board the bus to Rishikesh (255km, ~ 8:30 - 9Hours).
If you do not want to visit Mana village then leave Badrinath early in the morning and reach Joshimath from where you'll get the bus to Rishikesh.
Consider per person cost for about 14K.