If you use Chrome, there is an extension you can add on for free that's made for this stuff. It's called "Pixiv ugoira & manga downloader". When you open an animation on Pixiv, it will start loading its data. A series of three buttons will appear below the animation window after it fully loads (the little icon next to your address bar for the extension will have a number displayed over it showing the % progress if it's still loading). Until it finishes, there will only be one button. Wait until it finishes. It shouldn't take long. Then choose whether you want to convert the animation file into a .GIF or a .WEBM file. (I recommend you click "Generate WEBM", as .WEBM files are much better and provide much better animation playback.) When you select, it will begin, showing the progress of the process in place of the button you select. When it's done, it will change to say "Save" + whichever file type you chose. Click save, and you will be able to save it.