What were you hospitilised for? While I may not necessarily have the expertise to give recommendations based on your answer, it may affect your exercise options.
If you hadn't been hospitalised, here's the advice I would give you (warning, you're in for a massive information dump, so it's okay if you have to read over this a few times and ask some questions before it sinks in):
Cardio is actually not strictly important for weight loss or fat loss. You need to get your diet organised in such a way that you consume fewer calories than you use on a daily basis (cardio can help with this, by increasing the number of calories used each day, however strength training can do the same thing, and appears to be more metabolically beneficial [for weight loss] than cardio).
For fat loss, I generally recommend aiming to lose about 1lb/wk, which is the equivalent of about a 500kcal/day deficit. So if your daily metabolic rate (including training) is 2,000kcal/day, you'd be consuming an average of 1,500kcal/day. Granted, I don't know your actual metabolic rate, but that's a fairly common approximation amongst females. Pro tip: when losing weight, try to eat as much as you can while losing weight. It's good for your metabolism, will allow for longer progress, and will mean that when you stall you won't have to make drastic changes to break your weight loss plateau. So, if you can achieve weight loss on a higher calorie intake, milk that for all it's worth. Even though to lose 1lb/wk you should be eating about 500kcal/day below maintenance, if you stop losing weight, don't decrease intake by another 500kcal -- decrease it by only 100kcal, and see how you go: there's a good chance you'll return to regular weight loss patterns at that time.
Strength training will, in the best of circumstances, cause muscle mass to increase (which is needed for most people to experience toning -- 9 times out of 10, toning is the result of increased muscle mass and decreased fat mass; although if someone is already very muscular OR very skinny, they can achieve toning by increasing muscle mass OR losing fat (whichever is most appropriate) rather than doing both), and in the worst of circumstances prevent the body from losing muscle mass. The best of circumstances is when there's a surplus of calories in the body, giving fuel to grow; the worst of circumstances is when there's a calorie deficit, meaning weight loss is occurring. The implication here is that if you lose 10lb while strength training, more of the 10lb lost will be fat than if you lose 10lb without strength training, so you get a better quality of weight loss.
That being the case, it's time to learn some basic strength training techniques. I want you to spend the first and last 5min of each session focused on core activation drills/exercises, in which you focus on lifting your chest, setting your shoulders back and down, and drawing your lower abs and pelvic floor inwards. The exercises I want you to focus on for this are a standing posture set (just set up your posture as I've just described while standing), fitball rollout, side plank, and glute bridge. Make a circuit of those 4 exercises: 2 rounds at the start of the workout and 2 rounds at the end, giving 30 seconds to each (with side planks, make that 30 seconds each side).
Within the body of your session, it's time to get familiar with some machines. Ideally, you want to get to the point where you can competently and confidently perform freeweight exercises (squats, deadlifts, bench press, overhead press, pull ups, rows), but for now it's fine to learn with machines. A year ago I would have flamed myself for saying that, but I can easily list off about 20 things you need to learn to do with your body to do a good squat, and that's too much stuff to think about, so I'd rather you deal with machines where you only have to think about a handful of things, and get so used to the machines that you only need to think about 1 key thing for everything else to fall into place (this might take a month or two -- not a big deal in the big scheme of things).
So, here are the machines I'd have you using: Leg press, seated chest press, seated cable row, dumbbell shoulder press (actually not a machine, but in my experience much easier to learn than actual shoulder machines, so may as well get right into it), lat pull down, hyperextension (not really a machine either, but easy to learn), and standing calf raise. Perform 2 sets of 10 reps for every exercise, with 1min rest between sets. Start out with weights that are way too light to make sure that you can complete each set while focusing on technique, and add a little bit of weight each week. It'll get hard fairly quickly.
For each exercise, good technique begins with setting your core and posture, thus the core/posture drills at the start and end of each session. Chest up, shoulders back, lower abs and pelvic floor drawn in to make the core tight. In addition to this, your weight should generally be on your heels (this doesn't apply to calf raises).
For leg presses, drive your knees out (and turn your toes out slightly to accommodate this), and keep your shoulders and butt against the back rest at all times (people often allow their butt to lift up off the rest as they approach the bottom of the exercise -- don't do this, as it puts the back in a risky position). On squats and deadlifts I'd normally encourage you to lock out your knees at the top, but don't do that on the leg press, as it's very hard to unlock them again (as I've learned the hard way).
For chest press, again, bum and shoulders stay on the back rest. Keep your head up, too, to make it easier to keep your shoulders down and back and your chest up. Tuck your elbows down (this will help you to keep your shoulders down and back).
For seated rows, squeeze everything in towards the middle of your back and lead the movement with your elbows. Don't let your shoulders round forwards in order to get more range of motion. You should be opening your chest during this exercise, not closing it (which is what rounding the shoulders does).
For DB shoulder press, keep your glutes and thighs tight so that your whole body is a rigid pillar of tension from head to toe (this will help reinforce your core and posture, and will allow proper transfer of energy from your feet to the weights). Begin with the DB's touching the top of your shoulders and elbows under your hands, and press straight up, bringing the DB's together at the top.
For lat pull downs, use the knee pad for anchorage. Keep your chest up and lead the bar down with your elbows until it reaches the top of your chest. Contract your lats on the way down, and stretch them on the way up.
For hyperextensions, keep your trunk in good postural alignment, keep your core tight, and pivot at the hips rather than letting your back round. Use your glutes and think about driving your hips forwards rather than lifting your torso up. Aim to hyperextend your hips ever so slightly at the top, but don't hyperextend your lower back (this will require some solid ab activation).
For calf raises, keep it slow and focus on getting a stretch at the bottom. If you're doing these in the Smith machine, you can use this as an opportunity to learn where to load a barbell on your shoulders and how to hold a barbell that's there. There are a few places you can situate a barbell on your shoulders, but the easiest one for most beginners to learn is called the "high bar" position, in which you squeeze your shoulders back and contract your upper traps (the muscle from your shoulder to your neck), then load the bar onto your contracted upper traps. If you feel around the back of your neck, there's a big bone right at the bottom of your neck. You want the bar to be just below or behind this bone, held up by the muscle underneath the bone, not sitting on the bone. You want your elbows to be pointed down in line with your torso, and your hands to be as close together as you can comfortably get them. You also want your hands to be evenly placed on the bar (there are rough patches on the bar, called "knurling," to help you here, and they enhance grip), and your wrists to be straight. Any guesses why I'm suggesting you learn all this while doing calf raises, which, in themselves, require next to no thinking, instead of learning to do this during squats, which require a lot of thinking before you even touch the bar?
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Of course, depending on why you were hospitalised, some or all of this advice might become irrelevant.
Thank you in advance 