In English, the main verb usually tells you how someone moves, and a little word after it tells you where: run out, swim across, walk away, jump down. Spanish usually works the other way round. The main verb carries the direction (salir, entrar, cruzar, subir), and the manner is added afterwards as a gerund such as corriendo or nadando. So 'he ran out' becomes salió corriendo, literally 'he went out running'.
English speakers trip over this because they look for a Spanish verb meaning 'run' and then try to bolt on a word for 'out'. The result is understandable but sounds translated. Once you start with the direction verb, the sentence falls into place.
Word list
andarA1to walkvolvió andando = she walked backbailarA1to danceentró bailando = she danced incaminarA1to walkse alejó caminando = she walked awaycorrerA1to runentró corriendo = he ran inirA1to gofue corriendo a casa = he ran homeirseA1to leavese fue volando = it flew awayllegarA1to arrivellegó corriendo = she came runningnadarA1to swimcruzó nadando = she swam acrosssalirA1to go outsalió corriendo = he ran outvenirA1to comevino corriendo = he came runningvolarA1to flysalió volando = it flew outbajarA2to go downbajó saltando = it jumped downbajarseA2to get offse bajó del autobús de un salto = he jumped off the busbajarseA2to get outse bajó del coche de un salto = he jumped out of the carconducirA2to drivesalió del garaje conduciendo = she drove out of the garageentrarA2to enterentró de puntillas = he tiptoed inesquiarA2to skibajó esquiando = she skied downmanejarA2to drivesalió del garaje manejando = she drove out of the garage (Lat. Am.)marcharseA2to leavese marchó corriendo = he ran offregresarA2to returnregresó caminando = he walked backsaltarA2to jumpbajó saltando = it jumped downsubirA2to go upsubió corriendo = he ran upsubirseA2to get onse subió al tren de un salto = he jumped onto the trainvolverA2to returnvolvió nadando = she swam backacercarseB1to approachse acercó despacio = he crept upacudirB1to goacudieron corriendo = they came running (to help)alejarseB1to move awayse alejó caminando = she walked awaybrincarB1to jumpentró brincando = she skipped indescenderB1to go downdescendió flotando = it floated downescaparB1to escapeescapó nadando = he swam awayescaparseB1to escapese escapó corriendo = he ran awaymeterseB1to get inse metió en el coche corriendo = she ran and jumped into the carpartirB1to leavepartió a caballo = he rode offpasearB1to take a walkvolvió paseando = she strolled backtreparB1to climbsubió trepando = she climbed upapartarseB2to move awayse apartó de un salto = he jumped asideaproximarseB2to approachse aproximó nadando = it swam uparrastrarseB2to crawlsalió arrastrándose = he crawled outatravesarB2to crossatravesó el bosque a caballo = he rode through the forestcruzarB2to crosscruzó la calle corriendo = she ran across the streetdanzarB2to dancesalió danzando = she danced out (literary)fugarseB2to fleese fugó = he ran off (escaped)gatearB2to crawlsalió gateando = the baby crawled outhuirB2to fleehuyó = he ran awaynavegarB2to sailcruzaron el estrecho navegando = they sailed across the straitpatinarB2to skatecruzó el lago patinando = she skated across the lakecabalgarC1to ride a horsese alejó cabalgando = he rode awaycojearC1to limpsalió cojeando = he limped outrenguearC1to limpsalió rengueando = he limped out (Lat. Am.)
How it works
Build the sentence in two slots. Slot one is a path verb that says where the movement goes: out, in, up, down, back, across, towards, away. Slot two is optional and says how: a gerund (corriendo, nadando, volando) or a short phrase (de puntillas, a caballo, en bici, de un salto). If the manner is obvious or unimportant, you can simply leave it out.
El niño saliócorriendo de la casa.
(The boy ran out of the house.)
Cruzó el río nadando.
(She swam across the river.)
Rule of thumb: when the movement crosses a boundary (into a room, out of a building, across a street, over a border), Spanish strongly prefers the path verb. This is a tendency, not a ban. A manner verb is perfectly fine when you only add a direction or a goal, as you will see below.
The words
Path verbs: the main verb
These verbs say where the movement goes: salir (out), entrar (in), subir (up), bajar and the more formal descender (down), volver and regresar (back), cruzar and atravesar (across, through), acercarse and aproximarse (up to, towards), alejarse and apartarse (away, aside), llegar (arrive, come up), irse (off, away), and huir and escapar (run away, get away). Further examples are pasar por delante (go past) and meterse de un salto (jump in).
Entróde puntillas para no despertar al bebé.
(He tiptoed in so as not to wake the baby.)
Subí las escaleras corriendo porque llegaba tarde.
(I ran up the stairs because I was late.)
El perro se acercódespacio a la puerta.
(The dog crept up to the door.)
Los ladrones huyeron en coche.
(The thieves drove off. / The thieves got away by car.)
Manner verbs: the gerund
These verbs usually become the gerund in slot two: correr (corriendo), nadar (nadando), caminar and andar (caminando, andando), volar (volando), saltar and brincar (saltando, brincando), gatear (gateando), arrastrarse (arrastrándose) and trepar (trepando).
El gato bajó del tejado saltando.
(The cat jumped down from the roof.)
Se alejócaminando sin decir nada.
(She walked away without saying a word.)
Volvimos a casa andando.
(We walked back home.)
El pájaro salióvolando por la ventana.
(The bird flew out of the window.)
El bebé cruzó el salón gateando.
(The baby crawled across the living room.)
Watch out
The typical mistake is a word-for-word phrasal verb: corrió fuera de la casa for 'ran out of the house', or nadó a través del río for 'swam across the river'. A Spanish speaker will understand you, but it sounds like a translation. Say salió corriendo de la casa and cruzó el río nadando instead.
Manner verbs are still fine with a direction or a goal when no boundary is crossed. Prepositions like hacia (towards), hasta (as far as) and por (along, around) work well with them.
Corrió hacia la puerta.
(He ran towards the door.)
Some path verbs already contain the manner, so the gerund is often unnecessary. Huir and escapar already suggest speed, so huyó alone is enough for 'he ran away'. Llegar corriendo is the natural way to say 'come running'.
Summary
When English says how and then where (run out, swim across, walk back), Spanish says where and then how: pick the direction verb first (salir, entrar, cruzar, subir, volver) and add the manner as a gerund (corriendo, nadando) or a phrase (de puntillas, a caballo), or leave it out. This matters most when someone crosses a boundary. For a simple direction, corrió hacia la puerta is fine.