I want to upgrade graphics card on HP Slimline 410-030 Desktop



You'd have to check inside the computer or online how many watts the power supply is rated for and also look inside to see how much space is available for a graphics card. I would think that you'll be able to install a GTX 1050/ RX 460 at best.
 


It has this "180 W SFF Bronze internal power supply"
 


I looked into that PC model some more and I think that you should be able to use a GTX 1050, and I wouldn't recommend anything that draws more power. Something like this one should be ok: https://www.newegg.com/Product/Product.aspx?Item=N82E16814137058&cm_re=gtx_1050-_-14-137-058-_-Product

Upgrading to that graphics card would simply involve plugging it into the PCIe x16 slot on the bottom of your motherboard and installing the graphics drivers after that.

If you want something more powerful, I would advise looking into a PSU upgrade.