In instances like the texas revolution against mexico, in honduras with General Christmas, and in Niceragua, how did they get, if they did get, cannons, and any other weapons that a regular store wouldn't carry.
Do you mean a regular store, as in weapon's store? Almost all cases of heavy artillery being held by revolutionary forces comes from capturing said pieces, either in the initial stages or during the ensuing conflict. This link gives a bit of background on this, as well as speculates on why certain battles were fought during the Texan Revolution.
The alternative is foreign aid. In the case of the Revolutionary War for example, the French sent a significant number of artillery pieces to the Americans.
In short, the how was through aid or opprotunism. The issue, unfortunately, is that these irregular forces not only faced the difficulty of obtaining the ordinance pieces, but the actual ordinance itself as well, and often they possessed cannons they could not use. However, holding on to these pieces was often just as important as actually firing them, since every piece you took from the enemy was one that you deprived them of using, the logic in spiking (destroying) any artillery you had to leave behind on the battlefield.
In the case of the Texicans:
The famous cannon from the Battle of Gonzales (the one adorning the "come and take it" flag) was on loan from the Mexican government to aid in fending off local natives.
Besides that, as /u/spoonfeedme pointed out, they were generally captured. The MExicans left behind their cannons at the seige of Bexar and they were subsequently used to limited effect at the Alamo, for example.