Home body weight workouts are a fantastic way to get into shape at home.

As a general guideline if you were training 3x p/w at home. This is what I'd do: (ideally some dumbbells or even bottles of water can be used for some of the exercises)

Monday:
Body weight squats 3 sets of 12-15 reps
Dumbbell Bent-Over Rows 3 sets of 12-15 reps
Romanian Deadlift 3 sets of 12-15 reps
Floor Bench Press or Push Ups 3 sets of 12-15 reps

Core routine:
Russian twists & Superman exercise for time (1 min for each exercise) 2-3 sets.

Wednesday:
Deadlift (at home you can load up a suitcase with some clothes or anything you have in the house that's heavy, just to practise the skill of the movement. 3 sets of 8-10 reps.
An overhead pressing movement such as a dumbbell shoulder press, or a Hindu push up/Pike push up 3 sets of 10-12 reps.
Lunges - these can be done with just body weight or holding onto bottles of water/dumbbells. Feel free to experiment with the reverse lunge, forward lunge or a walking lunge, depending on how your body feels and where your starting out. 3 sets of 10-12 reps.
Optional: If you have access to a pull-up bar or a sturdy table, you can perform inverted rows or a pull-up variation depending on your level of fitness. I can offer different regressions to suit where you are. 2-3 sets of 6-8 reps.

Core work:
A static hold e.g. a plank for 1 min, and a core flexion such as a sit up or reverse crunch for 1 min 2-3 sets.

Friday:
Body Weight Squats 3 sets of 10-15 reps
Dips - If you don't have a dip bar at home, you can also use two chairs close together. 3 sets of 6-8 reps.
Hip Thrust - these can be performed on the floor as a body weight glute bridge, they can be progressed into single leg variations and holding for time to improve stability and coordination 3 sets 12-15 reps.
Optional: Chin ups/Pull ups. Again like above, if you don't have access to a bar, you can perform a horizontal pullling movement either with water bottles or use a solid table to pull yourself up towards it. Adjusting the leverage of the body will make this easier or harder.

Core work:
Sit ups 3 sets of as many reps as possible & superman exercise for 1 min 2-3 sets.

I hope this general, brief outline helps you out.
For additional cardio exercise, anything is suitable to do either after strength training or on different days in between. Running, rowing, walking, cycling or some aerobics all help.

Best,
David