It's a little different with everyone, but the feelings are generally the same. I definitely recognize stupors of thought. When the process becomes confusing, it generally means I need a new approach. Sometimes the answer to very important questions, especially where matters of stewardship, testimony or blessings are concerned it's burning of bosom. Sometimes it's a very clear and distinct impression that simply drives away all other thoughts. The answers vary as much as the situation.
Burning in the bosom usually comes when a confirmation is needed. For example, I've been in leadership positions where I have needed to make important decisions. After I have thoughtfully and prayerfully come to a conclusion the answer comes with that burning. If it doesn't, then I continue until I receive that confirmation. Another example was when I prayed about the choice I made about marrying my wife. I still remember that night 18 years ago. The spirit was so powerfully strong and it lasted for several minutes. I stood up from my bed and walked around my room and it was like the whole room was on fire. I knew that Father in Heaven approved and today I realize that the powerful answer served to reinforce my decision because of the really bumpy roads that my wife and I endured in later years.
Other times when I pray about something, my mind just seems to remain fixed on the answer as if none of the other options seem right. It's that 'I feel it with every fiber of my being' feeling. I've often prayed whether or not to continue in my line of work, which is very seasonal and not always dependable. But each time that I pray, nothing else seems right, even after studying it out in my mind as the Lord often councils.
Then there are the times when I just need a little wisdom and the answers come as thoughts. I have learned to tune in to the Spirit and one thing about me is I'm really a very weird ADD kind of guy. My mind is always going a million miles an hour, I tend to jumble my thoughts all the time because I usually think in terms of images rather than words or sentences. I even have a hard time "pronouncing" words in my mind because I think too fast. This is probably why my family thinks I'm crazy sometimes. My point is there are those quiet times when an answer comes to my mind in such a clear and articulated thought that I just know it didn't come from me. It is such a distinct whisper/thought that seems to instantly push out all the "noise." That's the best way I can explain it.
The common denominator with all of these experiences is continually pondering my solutions, studying them out in my mind and considering the best choice or choices. Afterwards, comes the fervent prayers alone in my room or my closet. I've spent many hours in my closet and have even fallen asleep in it before after spending so much time in there. We really need to have faith and not doubt God's power. Fasting is also an important tool in seeking the Lord's council. Consider Enos' prayer in the BoM, also Alma's. He prayed and fasted for many days (Alma 5) before finally getting his answer. Cornelius the Centurian and Gentile had such faith. He fasted and prayed for four days (Acts 10) before Peter was sent by the Lord to teach and baptize him. The Lord will always answer us, but it is always in His time, not ours and the answer isn't always what we think is best but what the Lord knows is best.
Ask and receive, not doubting!