So, some things to consider which might help you.
The 4 main attributes that determine "obedience" besides the actual obedience value are Awareness, Taming, Habit and Devotion.
There are also fear and despair, but in general these are detrimental for a lot of things, especially despair, so you don't want to rely on being cruel unless you know how to manage it.
The best way to get a slave to obey depends a bit on their starting values and personality, but in general you want to avoid building up significant despair or her mood will tank and she will hate you. This means no raping her, and no punishments that exceed the guilt value shown. If her portrait has "Guilty (1)" under it, only do a punishment with a value of 1, don't be extra harsh.
When you learn to cast magic, you can use a spell called Auspex which lets you examine all these values, by the way.
For taming, an easy way to get some points fast is to put her in a deprivation suit and/or pony harness/plumed bridle at bedtime. I often start new slaves with all three, and usually its good to throw them in the cells with no food for the first night too. You might get one despair from this but it will go away fast if you don't do anything else harsh afterwards. Also remember to give them some extra early awareness by explaining their situation on the first 3-4 days or so (the dialogue button next to slave portrait, choose to explain their position). Habit is mostly about getting the slave to regularly agree to follow orders, it will build up naturally as you do training, not much need to focus on it specifically. Awareness will also level up slowly by giving her punishment and reward which is proportionate, and other natural activities. Therefore the easiest one of the three "feeder attributes" that influence devotion is taming, because you can put her in special bedtime outfits to increase it rapidly.
Building up taming/awareness/habit will feed into devotion slowly, and devotion is the main attribute you need to increase to make slaves more loyal. You can't easily increase devotion by itself, there are some high level rewards/magic spells that give small increases, and a one time per slave potion called Philtre which you can make later on which gives some boost to devotion as well (usually better to save it for a boost on level 2->3 or 3->4 devotion with the potion, instead of using it right away at level 0 to get quick level 1, though).
Devotion can often take quite a while to start increasing, but in general you should be able to get up to 3 or 4 devotion points within about one to two months, depending on your skill and your slaver's attributes/access to magic. If a slave is particularly troublesome due to built up despair and you can't get a single devotion point within the first ~10-12 days or so, you might consider tossing her out to someone cheaply and starting over.
EDIT - Want to add a few other tips for newer players specifically that don't necessarily relate to devotion.
One, try not to get attached to your first few slaves. It's really important that as a new slaver, you start getting your reputation built up, and start selling slaves so you can get some capital for future training. Don't try to train up a B+ slave on your very first slave unless you know what you're doing, it's really best to churn out C+ quality slaves for a few rounds and then move on to B+ and A+ slaves for nobles, but don't be ashamed to put out a few D+ slaves as well if you need some quick sparks to sustain yourself early on.
Two, the earlier you manage to get the Bull Ring from the House Taurus noble in the central forum (white district sub area), the easier the rest of your game will be, so try and fit in an arena champion slave somewhere in your first 2-300 days of playing at least. You won't get paid any sparks for this slave, just the artifact, so you need to build up some cushion to afford this, but it'll be worth it in the long run if you can do it.
Third, fear and despair are really only useful when trying to break particularly prideful slaves, or because you want to be an asshole for roleplay reasons. 95% of slaves should really never be given despair beyond 1-2 points, if you get to more than that you're probably being way too hard on them. Fear is usually fine in moderation (try not to get it all the way to 5, but 2-3 points is usually a good thing early on) and can be balanced with other mood boosts, but despair will quickly make slaves extremely depressed or even suicidal/try to attack you, and it eats away their devotion gains and makes it take much longer to train your slaves. It just sucks. Try to avoid despair as much as possible, seriously, anally raping your slaves on day one might seem like a power move or something but trust me it really isn't a good idea unless you're trying to break a red pride slave as fast as possible and know how to get rid of 4 despair points without killing her by accident.
Fourth, make sure to train a competent assistant as fast as possible. The starting assistant will be very helpful, but I usually make one of my more promising slaves into a replacement and cryo-stash the starting assistant at some point. Having an assistant with S+ Cooking/Maid/Nurse/Secretary is going to make your life a *lot* easier, try to get those 4 maxed as soon as possible at the least. Nurse will let you keep slave weights constant, once you get to "model" you can set calculated diet and never have to pay for a nutritionist if your assistant has medical skill. Secretary will let your assistant be your bookkeeper, and give you lots of extra cost of living savings every decade. Maid/Cook lets you delegate this stuff to your assistant, meaning more time for training your slaves and less grumbling about the housework for your slaver. Other skills have uses too, but those four are your assistant's core functions aside from training/supervising your slaves.
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Here is an example of a pretty much ideal situation following the first week of training, what to aim towards for attributes. You can see this screen if you cast the auspex spell, which will be available to cast as soon as you purchase and wear wizard robes. Note that this slave started with 3 habit so she would probably only have 2 points by now normally. Taming is usually the highest of the three but you need to get them all up in balance to get devotion ticking upwards daily.
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This is the example of the "I want to tame this girl immediately" suit, feet don't matter so might as well give her mood boosting slippers once she earns them as a gift but the rest will increase her taming nightly. Remember to take her out of it during the daytime to help her mood during trainings unless she starts to like it or something, certain slaves like either pony gear or being bound but most will get mood penalties. The piercings also contribute to taming if you have a full set, you can get them from the Necropolis district at the Steel Rose.
