It has been about two months since I've started learning English conversation, but I still don't feel much of an improvement.
ご質問ありがとうございます。
"It has been about two months"=「二か月ぐらいになります」
"since I've started learning English conversation,"=「英会話を学び始めてから」
"but I still don't feel much of an improvement."=「でもあまり上達した感じはしません。」
ご参考になると幸いです。