Something you could do is download Optifine for whichever version of Minecraft is running. This offers you increased performance with your current setup, as you're able to edit a wide number of settings. As SirBarasco and BizaJR stated, outside of that, you may have have to look into contacting your internet service provider about your current internet speed; or look into an upgrade for your system to run Minecraft better.
Hope you can get your situation figured out. Have a good day!