I've seen many people fail at conversation because of their pronunciation. Even if the vocabulary and grammar are correct, sadly, the people they are talking to are sometimes not willing (or able!) to do the work to understand what they are saying if the accent is difficult to understand or the intonation is off. But don't stress, pronunciation does not need to be perfect but improving it helps a lot!
Here are some tried and true tips for improving your accent that you can do on your own!
1. Practice individual sounds that may be a problem. For example "r" or "l" for Asian speakers, or "th" for french speakers.
2. Find a native speaker saying a poem or speech on the web and the transcript for it. Political speeches are a good choice. Listen to the native speaker. Memorise the speech. Tape yourself and compare yourself to the native speaker. Note which words are a problem and focus on them. Repeat! Repeat! Repeat!
3. Read passages from a book or newspaper out loud. Most people forget that you use muscles to form sounds. Some muscles may not be used in your native language but are needed in the target language. This is a good way of working those muscles.
4. Do not forget about intonation! Each language has a different rhythm and emphasis. You will be more easily understood if your intonation mimics that of native speakers.