First, you need to know how much DNA you need to send for sequencing. Then, run a gel with your DNA that is at least 5 times higher than the required DNA concentration for seq. Cut the band from the gel and extract the DNA using DNA gel extraction kit (e.g. https://www.qiagen.com/us/shop/sample-technologies/dna/dna-clean-up/qiaquick-gel-extraction-kit) . Measure your eluted DNA and send the right amount to the sequence. Good luck
I'd suggest you talk with a colleague so they can give you some practical advice (what percentage gel to use, which gel combs, etc.). You'll need access to a UV transilluminator, a sharp blade to cut the agarose, and a method to purify the DNA from the agarose. I also recommend the Qiagen kit. Good luck!
Please find someone around who has some practical experience and can show you the technique. As Ahmed E. Dhamad suggested we usually run a gel with more DNA than the required for sequence, cut bands and use kit for DNA extraction.