My answer in one word would be the Quran.
Quran: Miracle of Prophet(pbuh)
The only miracle that the Prophet(pbuh) left Muslims with is the Quran. So by reading and analyzing this Quran, you can assure yourself that you are on the right path.
A person can also assure themselves by implementing the Quran in their life and see the transformation it brings.
A) Assure yourself by: Analysis of the Quran
The Quran repeatedly calls people "men of understanding" , this simply implies that we are expected to analyze the message of the Quran.
In one of the verses the Quran goes way out to challenge everyone to analyze the Quran.
Then do they not reflect upon the Qur'an? If it had been from [any] other than Allah, they would have found within it much contradiction (Quran 4:82)
Today you can pick up books of any religion and you will see many scientific errors and internal contradictions in them. But this is not the case with the Quran.
Many facts mentioned in the Quran (like motion of the sun etc) are "advance facts" because they are recent discoveries by humans but have been a part of the Quran since 1400 years.
B) Assure yourself by: Implementation of the Quran
When people implement the simple teaching of the Quran in their life, you will actually see transformations happen to individuals & societies.
For example:
Praying 5 times will reduce you chances of back or knee problems.
Eating halal will not transfer germs from blood of animals to you.
Fast in ramadhan to increase intestinal absorption.
Pray in the mosque as one ummah with others and it will reduce racism.
Dont drink alcohol, this will keep your brain healthy.
..and the list goes on