Designing the logo needs creativity and unique yet relevant that it is in sync with the company.
Just look at the bullet train logo, the cheetah, the outline of the train looks so simple but is very effective.
Many prefer the Adobe Illustrator or Adobe Photoshop. If you are using this, have the basic idea in your mind or hand-drawn images the open a new file and try out the various combinations with respect to images/words/color etc. Earlier pirated versions of Abode used to be available. Now it is very difficult and everything is online and for 1 year with auto renewal. For the illustator is is around 16,000/year, for creative cloud/photoshop it comes to around 8000/year.
Corel Draw is good for beginners with light drawing and easy editing tools and is recommended for vector drawings.
Jetta Logo Designer is also good for beginners with around 400 templates and 5000 icons/forms that you can experiment with.
Logomaker has a trial version that you can experiment with and is very easy and less time-consuming.
If you are serious, the tips would be to have an original concept, do not rely on colors and stun effect, keep the ratio of proportions clear with words and shapes and go for an affordable professional one. Some computer centers/ digital studios allow students to use their legal software for a small price, you can try this.