ANSWER:
First of all, think about the Bais Hamikdash; most people don't even think about it. When you finish Shmonei Esrei, say the last few words…yehi ratzon milfanecha, Hashem Elokeinu Ve'lokei avoseinu sh'yibaneh Bais Hamikdash b'mheira vyameinu....say it with kavono! Say these words, show that you understand that it's a loss. So every day when you finish Shmonei Esrei, say these words, that's number one.
Also, if you can think how great was the opportunity when the Bais Hamikdash existed, and you would come to the Bais Hamikdash and you would learn yiras shamayim just from looking at it, l'maan tilmad lyira es Hashem Elokecho kol hayomim, merely by coming thereand seeing kohanim b'avodosom, u'leviim beshira u'vezimra...you would become so inspired.
You know, Yonah Hanovi became a navi because he was at the simchas beis hashoeiva at the Bais Hamikdash, and he was so inspired that the ruach hakodesh came upon him; he became a navi.
Therefore say, Ribono Shel Olam, restore the Bais Hamikdash, we want Moshiach! The Bais Hamikdash without Moshiach is also good. Moshiach will build the Bais Hamikdash again. We should all come together in the Bais Hamikdash, and we'll get ruach hakodesh from being there– that's why we want the Bais Hamikdash.
Little by little that's the way to mourn for the Bais Hamikdash. You'll never mourn for it if you don't feel the loss. So first you have to train yourself to feel how great was the opportunity when we had it, and therefore you'll know what it means that you don't have it, and you'll mourn for the loss.