If it’s a conspicuous species like with a lot of eggar and tiger moths you can usually spot them resting in plain sight on foodplants or basking in the open during sunny days after their winter hibernation
noctuids are also fairly easy but you normally need to go out with a torch after dark to look on low growing plants where they’re usually quite obvious
geometrids are tricky since they blend in well with hostplants and their surroundings but can usually be found if you have a sharp eye and don’t mind foraging around shrubbery and trees
hawkmoths are also fairly easy to spot but I’ve only ever seen them feeding after dark where they’re most obvious since during the day they stay quite tucked away in foliage (except when they’re ready to pupate and they’ll be very conspicuous wandering around open areas)
for most of the micro moths (as a blanket term) they’re usually extremely tricky to find as caterpillars and most of them are tricky to distinguish but many of them live in rolled up leaves.
tussock and prominent moths are fairly easy to spot if you look for them like with hawkmoths
as a general, look for holes and chewed up parts of leaves as well as around unusually bare areas of a plant (sometimes confused with slug damage tho), search at torchlight for any nocturnal caterpillars, look for prepupal catties wandering around looking for a pupation site, look on fences, tree stumps, under rocks etc for any caterpillars around and if possible try and take a few home with their foodplant to raise into moths so you can figure out the species (don’t over collect and if they don’t do well with you release them back where you found them).