You have to inform your employer of your plans regarding resignation 30 days prior to such, and nasa ating labor code yun. Liable ka for breach of contract of employment sa employer mo, especially if they find out that you left them and went to another employer. They can sue you for damages, and rightfully so since effectively nag-AWOL ka sa kanila and lumipat sa ibang employer. May sinusundan kasi tayong due process when it comes to resignation of employees, since hirap din yung employers na maghanap ng kapalit mo, training them again and all.
Ayusin mo muna yung sa previous job mo. Render ka ng 30 days and tapusin mo lahat ng clearance procedures para malinis yung pag-alis mo sa previous employment mo. Make sure to ask the HR of your previous employment kung meron ka pa bang kelangan na gawin na procedure as per company policy to render effective resignation. Kunin mo na rin kung ano pa yung kelangan mo, like Certificate of Employment and whatnot. Your previous employment may become an issue with your new prospective job kapag nalaman nila na di ka nagresign ng maayos sa dati mong trabaho.