Many people confuse supposed to with suppose to and used to with use to. However, the correct way to use both is with the 'd' on the end. When spoken, it's often difficult to hear the 'd' on the end of supposed to and used to, especially because it's followed directly by the 't' sound in to.
1. Supposed is an adjective meaning 'required' in this context. Always use the adjective form supposed anytime the word to directly follows it.
"I'm supposed to go the store." or "What am I supposed to do?"
Suppose is a verb meaning 'to think' or 'what if'. However, the word to wouldn't be used after the verb suppose.
"I suppose she's right." or "Suppose they don't show up."
2. Used is a verb that shows past tense. The first sentence below is normal past tense; the second sentence is in negative form because never is in the sentence directly before used to.
"I used to drink soda." or "They never used to travel."
The exception and only times use to is appropriate instead of used to is when it's used in negative form with the word didn't directly before it or when it's used in question form.
"They didn't use to travel." or "Where did you use to travel?"
Overall, always remember to use supposed to and used to WITH the 'd' on the end. The only exception is when used to becomes use to in question form or negative form ONLY with the word didn't directly preceding. Luckily, the majority of the time the exception isn't used and it's not a problem.