Is that 10kg total? Or 10kg plus the barbell (which, if it's a standard powerlifting or Olympic barbell, should be 20kg)? For how many reps? And how many sets?
Since your current number is 10kg (however you've got that worked out), I'm going to make the assumption that you haven't done much squatting before, and probably haven't had much coaching on the exercise. So, for some (relatively) quick instruction, a while back. Obviously, you won't need to read the sections on front squats and overhead squats - just the stuff on back squats. It's far from perfect in that it doesn't tell you everything I could tell you about squatting and how to get it right, but it should give you a reference point to make sure you're on the track. I'm emphasising this first before I even mention exercise programming to achieve your goal because a lot can go wrong when a squat is poorly performed, which 99% of gym squats are.
Alright, onto programming. The main exercise to get your back squats up is, shockingly, back squats. I recommend doing them 3x/week. Most people will tell you that's way too much squatting. Most people have piss weak squats. You do the math.
Start out with bodyweight squats. Hips below parallel, lower and upper back in proper extension, driving through the glutes and the heels all the way up to the top. When you can do 3x10 bodyweight squats with decent form, add in the barbell for 3x5. You should be able to get bodyweight form down in a single session, so you should have the barbell across your shoulders on the second session after a couple warm up sets with bodyweight.
On the 3rd session, you will do 5x5: 2x5 with the barbell, then 3x5 with 5kg on the bar (25kg total).
For the next 3 sessions, you will add 5kg to your work sets, every session, while adding 1 additional warm up set. The next 3 sessions should look like this:
1:
2x10xBW
2x5x20kg
1x5x25kg
3x5x30kg
2:
2x10xBW
2x5x20kg
5x25kg
3x30kg
3x35kg
3:
2x10xBW
2x5x20kg
5x25kg
3x30kg
2x30kg
3x5x40kg
That's the first 2 weeks covered.
From here on after, add 2.5kg/session to the 3 working sets. Keep all warm up sets, always starting with bodyweight then 20kg. However, as the working set weights increase, the warm up set weights will become spread out a bit more.
For example, at 60kg (working sets), the session should look like this:
2x10xBW
2x5x20kg
5x30kg
3x40kg
2x50kg
3x5x60kg
If you miss any reps in the working sets in the first 2 weeks, repeat the session again next time, then cut back immediately to 2.5kg progression afterwards, rather than maintaining 5kg jumps. If at any point you miss any reps after a 2.5kg jump, stay at the weight for as many sessions as it takes to successfully get 3x5 at that weight, then increase the weight on the next session. Every time you get 3x5 at your working weight, you must increase the weight in the next session, even if it means you only get something like 5/4/3, etc. If a week goes by without getting all reps, decrease the working set weight by 15kg and work back up. If a rep is performed with bad technique, don't count it, and finish the set right there. For example, if you do 2 good reps, then 1 dodgey rep, rack the weight and call it a set of 2.
Once you can do 3x5x85kg, you should (in theory) be able to do 1x100kg, but still work up to it so that your body's ready to lift 100kg. If you get 3x5x85kg and you want to test your strength asap, then next session do 2x3x90kg, then 2x2x95kg the following session. If you get all reps on these two sessions, take a few days off, then come back in and test your 1RM.
Other useful exercises to help with this goal are deadlifts, and to a lesser degree leg presses, lunges and hyperextensions/GHR's. But ultimately, you squat to squat, you deadlift to deadlift, you bench press to bench press, you pull up to pull up, you run to run, etc.
Finally, make sure you eat. If you aren't eating right, you can't recover right, which means you won't be able to keep on progressing from session to session. Eat lots of meat and vegetables. Eat fruit, nuts and eggs. Have some carbs for energy, to help build the muscle fibres that'll be lifting that heavy weight on your shoulders. Drink a lot of milk. Strength will come most quickly when you lift hard and eat harder.
