Generally speaking, co-opting the (recently conquered) locals goes a long way. Alexander was quite noted at the time for going out of his way to adopt local customs (some of which his Macedonian citizens didn't agree with) to make those new connections a bit more solid. The Mongols regularly conscripted troops from conquered territories (pretty much the origin of most of their infantry), and (at least over time, and in some places) adopted local customs as well to make things easier. Even places that conquered a little slower needed to use local troops to maintain order, especially if there were large differences in population; England's use of sepoys, for example, or Rome's auxiliaries.

There's a pretty simple formula for a conqueror's success:

(1) Conquer someplace.

(2) Install your own lords/governors, and make sure they have enough loyal troops (typically from your nation) to maintain order.

Thankfully for the conqueror, you often have more soldiers than you need to maintain order. For example, even 1% of your population is quite high for military service (and, frankly, it's difficult to support more at least until after the agricultural revolution), but if it's for a limited period of time and you're willing to let the situation at home deteriorate, then you can even manage 2% as Louis XIV did. On the other hand, enforcing order afterwards may need closer to 0.3% (about what the US does currently for policing); communities back then were largely agrarian (about 75% of population for most pre-agricultural revolution societies) and had very low mobility. So, that leaves you with 2/3 of your troops (or more) to keep conquering.

(2. a) At the same time, co-opt as much of the local leadership as possible.

Intermarriage, vassalage, hostages, taking their nobles' household troops and replacing them with a number of your older veterans (so you have troops, the local now-cooperating mid-level government maintains order, but are reliant on your men to do so), and settling your older troops as gentry/farmers (as the Romans did) are all good options.

(3) Take all the local troops you can. Maybe conscript some.

At the end of the day, it was hard to start a good rebellion. 75% of a conquered population are scattered around the countryside in packets of a few hundred, and they need to work to eat. Meanwhile, cities and towns can supply people who aren't needed to maintain food security, and can rapidly produce weapons, but they need to win pretty quickly, or else the food supplies stop and the cities starve. So most potential revolts are poorly equipped and trained, and in little penny-packets, or centralized to a few cities where the conqueror controls the fortifications and can surveil troublemakers. A medium-sized well armed group of bloodied troops can smash dozens of smaller groups of revolting peasants who don't want to be conscripted, even if all together they might outnumber the troops massively. If it's a more feudal situation, the local lords may not cooperate together very well, and again if the conqueror can beat their field armies, they can definitely beat the scattered remnants and those forces which weren't originally called up.

Either way, the conqueror takes those people who are most suited to becoming the nucleus of a resistance, and brings them with their army (which already beat them). Loyal troops from the homeland are placed in command of conquered troop formations (again, divide and conquer). And when the conscripts finally are fighting in the next nation over, well, odds are those nations weren't friendly to start with, the conscripts don't speak the local language, and have either just finished beating or being beaten by the locals. None of that makes it likely for the local people to support deserters or mutineers.

(3. a) Make an example of anyone who is troublesome. Then make sure everyone knows about it.

(4) Conquer somewhere else. You can use a mix of your own troops (for leadership) and your previously conquered troops to control this new region.

Again, the troops from the previously conquered region are unlikely to be super supportive of the newly conquered people (also, may be selected for a more authoritarian and loyal attitude), and the newly conquered people are unlikely to be supportive of the previously conquered troops who they now see as occupiers. Mutual hostility will enforce this divide and further separate the two groups of people and their interests.

(5) Rinse and repeat.