Learn the reasoning behind a solution and how they derived that solution. After a few days, go back and solve the same problem again from scratch without any reference. Even if you remember the gist of the solution, you would still have to implement it again, which can be a challenge. You can also look at the solution in a different language and code it in a language more familiar to you. Understand the thought process behind a solution and how to derive it. Ideally use only the hints so you don’t look at the complete solution and have the chance to solve the problems on your own. But the goal is to reach a state where you can come up with optimal solutions without looking at the answer. This just takes practice and time.
Build a solution from scratch. Get into the habit of getting your implementation to work. If you have difficulty to get it to work, you can then rule it out and move on to another approach. Speed should not be the focus. Developing a method of working through the problem in a methodical way with a set number of steps is the goal. Speed will be a byproduct of refining your method of approaching a problem you've never seen before.
Part of the process is working through frustration, finding a starting point and building confidence in your solution. You must expect to work through those uncomfortable moments. Do not look at the solution until you have your own working implementation. Do not write a single line of code until you have written what you think is an entire working solution on paper.
If you are passing some of the test cases and can't think of any other solution after spending a significant amount of time on it then look up the solution. Read the algorithm and then implement it. Do not look at the solution and copy and paste the solution in to add a +1 to your record.
There's no short cuts. It's hard work, discipline and spending time working through it. The point isn't solving the problem. The point is improving your problem solving skills and communicating how you're going to approach the problem before writing code.
The hard part isn’t solving the problems themselves, but rather overcoming the mental barriers and having the discipline to solve the problems consistently.