They were used as cannon fodder (worth far less than Republican regulars), and they often had no military background - especially those from the US (some ageing European leftists had seen action in WWI). The leftist government was quite willing to send them home when it felt the Nationalists might do the same with their Italian troops (which they didn’t); they were paper tigers who took losses but were ineffective against Franco’s regulars. Their real contribution was as propaganda tools (to give the appearance of a real international effort), but their numbers were small and they were often from countries that didn’t want them anyway.
There were no “Republican regulars”. The Spanish army was made up of conscripts with only a tiny “regular” cadre, other than the Army of Africa, Franco’s own creation, which really were experienced regulars. The Republican army in metropolitan Spain, after the coup, was a shambles. The officers were inexperienced and poorly trained, if they hadn’t deserted to the Nationalist side, there were few NCOs, many of the soldiers had deserted or joined militias, and morale was terrible. The International Brigades were seen as more reliable by far. Eventually the government integrated the army battalions with the militia.
The Republican government didn’t disband the International Brigades until after the Battle of the Ebro and the splitting of the front when the Nationalists cut off Catalunya. All hope was gone by then.
Most handy and very readable general history of the Spanish Civil War - “The Battle for Spain” (also published as “The Spanish Civil War”) by Anthony Beevor. The old classic by Hugh Thomas is more detailed than Beevor, lacking mainly a more inside look at post-Cold War Soviet information. I have about seven histories or pseudo histories of the war. But you should be fine with those two.
The Republican forces had next to no military background at all. The Spanish army was a bureaucratic mess and their conscript training was a shambles. Between the breakup of the cadre, as so many of the best turned nationalist, and the inability to mobilize conscripts, and leakage to all the militias... there was nothing, in spite of having the theoretical preponderance of weapons and manpower.
The Nationalists had almost all the real soldiers, between the Army of Africa and the metropolitan army units that stayed together as units, notably the cavalry under Monasterio. Even the Carlist militia had at least done something about getting organized and trained before the war broke out.