Assalaamu alaykum. I have two questions that I would like to ask you:
1) How can you explain to a person what Allaah is telling you to do? For example, I am supplicating Allaah to tell me what to do with a conflict that I am facing (I am not making Istikhaarah [prayer of consultation]). After supplicating, something in my mind tells me what to do on how to solve this conflict that I am facing. Does this means that Allaah gives me the idea to solve the conflict? I am asking this question because I already dealt with problems in my life and every time I communicated with Allaah by supplicating to Him and asking Him for His help, I got an idea on what to do each time I finished supplicating Him. I told a Muslim about this, and that Muslim did not understand me.
2) When a person is making Istikhaarah, how would a person know if what they ask for is working out? Will there be signs that will appear to that person that will inform them that they will get what they ask for or not?
Allaah willing you understand my two questions.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger. 

When you turn to Allaah in supplication and seek His help imploring Him to bless you with what is good for you and to safeguard you from harms, it is likely that He inspires you with a way out of your problem as you implore Him and turn to Him for guidance and aid. This calls for striving in expressing gratitude to Him and praising Him as befits Him. This is not a strange thing in the slightest; Allaah, The Exalted, answers the supplication of those in need who call upon Him and relieves the distress and harms. Allaah, The Exalted, says (what means): {Is He (not best) Who responds to the desperate one when he calls upon Him and removes evil?} [Quran 27:62] He also says (what means): {And when My servants ask you (O Muhammad) concerning Me - indeed I am near. I respond to the invocation of the supplicant when he calls upon Me.} [Quran 2:186]

What you mentioned is a manifestation of the kindness and mercy of Allaah and there is no difficulty in explaining that to others. Verily, the kindness and mercy of Allaah have no limits.

As for the Istikhaarah prayer, we believe that when the person performs the Istikhaarah prayer, he should go ahead and do what he is doing Istikhaarah about, and if he finds that the matter is facilitated, then this is a sign that this is good for him; otherwise, he should give it up and know that it is not good for him and be content with the choice of Allaah for him, knowing that it is definitely better for him than his own choice for himself. For more benefit, please refer to fataawa 82964 and 83982.

Allaah knows best.