kérek = I ask (for) = I would like. e.g. vízet kérek = I would like some water.
keresek = I am looking for, that is, actually searching for something.
szeretek = I like e.g. bört szeretek = I like wine, as in enjoying wine.
If you are on Mac or iOS then hold down the key you want to type, and once the accent options come up release the key and choose the accent you want. You can do them all except for ő and ű this way. On Mac/iOS, you can set up a text shortcut in settings for these characters (you can choose something unusual like ô or ooo or o"" to map to ő)
Or you can go into settings and add the Hungarian language keyboard. This works great for iOS and Android, not so much on laptop (since the actual labels on your keyboard don't change)