Take Juit ㅈ, Chiut ㅊ, and Ssang-juit ㅉ. The first is regular sound without emphasis or action in the pronunciation. The accent mark above it makes Chiut ㅊ and causes more of a Ch sound than the J sound of Juit ㅈ. To understand the Ssang consonants, imagine, just as King Sejong probably meant for it to be, that you have two of them immediately together, like if you were to pronounce the two d's in Daddy (say it like you were a toddler Dah-dee). Can you feel the small pause or closed-then-open accentuation (differing from the full accentuation a Ch sounds makes)?
So when you have Shiut ㅅ and Ssang-shiut ㅆ, the same things happens. The Shiut will have more of a relaxed pronunciation and come out with an Sh sound, whereas the Ssang-shiut ㅆ is going to be more like (at least a bit closer to) the sound of a snake with its high pitched Sss.
The same goes for all of the letters. Digut ㄷ, Tiut ㅌ, and Ssang-digut ㄸgive you (perhaps something close to) D, T, and Dd respectively.
Just remember that the consonant without embellishment is relaxed. With a mark on top it is strong and forced, like an explosion. Doubled, it stops-then-goes like a implosion-stop-pronouncing.